Dynamic Bandwidth Allocation in a Circuit-Switched Satellite Network:Provision of Deterministic and Statistical QoS guarantees

N. Blefari-Melazzi, M. Femminella, G. Reali

Dipartimento di Ingegneria Elettronica e dell’Informazione (DIEI)University of Perugia, Via G. Duranti, 93 - 06125 Perugia – Italy; E-mail: blefari@diei.unipg.it

Abstract -- Current satellite systems operate according to circuitswitching transfer modes. To improve flexibility and efficiency,several kinds of packet switching systems have been proposed [e.g.7,8]. However, it appears that full packet switches are stillconsidered complex and expensive, when implemented on board thesatellites. For the time being, a compromise has been found insatellite networks with Dynamic Bandwidth Allocation Capabilities(DBAC). Such systems are based on classical circuit switches, butthe DBAC payload allows changing dynamically the capacity ofeach connection, without the need of tearing-down and setting-upagain the connection itself.

In this paper we consider a DBAC satellite system and definealgorithms to allocate the bandwidth so as to provide deterministicand statistical QoS guarantees. The traffic sources are regulated bystandard Dual Leaky Buckets (DLBs).

We define bandwidth-handling policies, design ConnectionAdmission Control rules and evaluate analytically the systemperformance. As expected, the numerical results show a significantincrease of the overall utilisation factor of our system, whencompared with a plain circuit switching solution.

I. INTRODUCTION

This work is framed in the ACTS program ASSET (ACTSSatellite Switching and End to End Trials), sponsored by theEuropean Union. ASSET is based on the EuroSkyWay (ESW)Network [1,7], which is composed of a number of GEOsatellites, a Master Control Station (MCS, on earth), userterminals (mobile), earth stations (fixed), including a certainnumber of Interworking Units (IWU). These IWUs are stationsthat interface the ESW system with terrestrial networks (e.g.the Internet, ATM, etc.). In addition to its own protocols,which allow ESW users to exchange information amongthemselves, the ESW system is designed to support a variety ofcommunication paradigms (e.g. the Internet, the ATM/B-ISDNand the N-ISDN).

It is well known that packet switching provides flexibilityand efficiency. However, it appears that full packet switchesare still considered complex and expensive, when implementedon board the satellites (at least in the mid-term). In addition,circuit switching has still some attractions, at least forparticular services. For the time being, a compromise betweencircuit and packet transfer modes has been found in satellitenetworks with Dynamic Bandwidth Allocation Capabilities(DBAC). Such systems are based on classical circuit switches,but the DBAC payload allows changing dynamically thebandwidth of each connection, without the need of tearing-down and setting-up the connection itself. The ESW network isa DBAC system. In ESW, a common framing structure isdefined and applied to all the carriers. The smallest unit

switched within the system is the so-called satellite cell. Eachsatellite cell has a size equal to 53 bytes and provides a netinformation rate of 16000 bit/s (basic channel).

The traffic control methodology is similar to the one of theATM and to the RSVP paradigms (i.e. Declaration of Trafficdescriptors, Connection Admission Control, Policing). The set-up procedure is handled by the MCS; therefore the signallinginformation has to make two satellite hops (lasting two satelliteround trip times) to go from a terminal to the MCS and comeback. Once a connection is set-up, the Dynamic BandwidthAllocation Capabilities allow changing the bandwidth of theconnection itself by means of In Band Requests (IBRs). Eachuser can ask to increase or decrease dynamically (frame byframe) the capacity of a connection, according to his needs.The IBRs are sent to a module resident in the satellite andcalled Traffic Resource Manager (TRM). The TRM can acceptor not the IBRs. When a user requests a change of capacity, thenew value of capacity is effective only after that he receives apositive answer from the TRM. The latency of the proposedscheme is then equal to one satellite round trip time, ∆T.Thanks to the DBAC, the ESW remains a fairly simple system(the on-board switch is a simple T-switch) and yet it can offerincreased efficiency and flexibility.

In this paper we propose a resource management schemethat guarantees the user perceived performance and exploitsthe system resources efficiently. In particular, we definebandwidth-handling policies, design Connection AdmissionControl (CAC) rules and evaluate analytically the systemperformance. The structure of this paper is as follows. InSection 2 we introduce the system architecture and theproposed resource management scheme. The ConnectionAdmission Control (CAC) rules are defined first withreference to each satellite terminal (in Section 3) and then atthe Master Control Station level (in Section 5). Section 4 and 6are concerned with the relevant performance evaluation. Someconcluding remarks are given in Section 7. An Appendixreports material not essential to the continuity of the text.

II. SYSTEM ARCHITECTURE

To simplify the system procedures we make twoassumptions:� the overall traffic is divided into high priority (HP) traffic

and low priority (LP) traffic. A given amount of resourcesis assigned to the HP traffic so as to satisfy pre-definedperformance. When the HP traffic is not exploiting all theallocated capacity, the unused capacity is temporarily takenaway from the HP traffic and used to carry LP traffic.

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When the HP traffic needs the capacity that has been takenaway, said capacity is once again given back to the HPtraffic itself, after a round trip time. Obviously, thesevariations of the capacity used by the HP traffic areperformed by means of the DBAC.

� the HP traffic entering the system is regulated by means ofDual Leaky Buckets (DLBs). A DLB implements jointlytwo Generic Cell Rate Algorithms (GCRA) [2,4]. TheDLBs assure that the traffic entering the system can becharacterised by only four parameters and greatly simplifythe three phases of a traffic control scheme, namely theTraffic Descriptors Declaration, the Connection AdmissionControl (CAC) and the Usage Parameter Control (UPC).The four parameters controlled by a DLB are: the PeakCell Rate and its Tolerance, the Sustainable Cell Rate andits Tolerance (or Burst Tolerance). The DLBs can be usedalso to smooth the incoming traffic.

With reference to the traffic coming out from a generic DLBand feeding the satellite network we denote as:- PS: the Peak Cell Rate (in cells/s);- rS: the Sustainable Cell Rate (in cells/s);- BTS: the Token Buffer Size (in cells) (i.e. a parameter

related to the Tolerance of the Sustainable CellRate, or Burst Tolerance).

We assume that the Tolerance of the Peak Cell Rate is equalto zero or included in the Peak Cell Rate parameter. Thanks tothe above assumptions, each HP sources is described by meansof three Traffic Descriptors (TDs) (i.e. PS, rS and BTS).

In the following we consider a generic satellite terminal(this can be a mobile terminal, a fixed earth station or anInterWorking Unit, IWU) and we assume that this terminalintends to generate a given amount of traffic towards thesatellite network. We assume that each terminal has a bufferdedicated to the HP traffic (HP buffer). We also assume that, ifvarious traffic sources belonging to the same terminal want toemit traffic towards the same destination, then they can bestatistically multiplexed over the same ESW connection. Thiscan be an unusual case for a mobile terminal, but it can be afrequent situation for IWUs or for connections carrying trafficon behalf of Service Providers. Note also that a satelliteterminal can support different “user terminals” (e.g. a numberof N-ISDN telephones), even physically disjoint from thesatellite terminal itself and abutted to the latter.

The system architecture of a satellite terminal (SaT) isshown in Fig. 1. For the sake of simplicity we consider onlyone ESW connection. The HP traffic generated by a SaT andsupported by the same ESW connection can be a superpositionof K heterogeneous traffic sources. An additional buffer (LPbuffer), can be eventually used by the LP traffic. The resourcemanagement scheme assures that the performance measuresperceived by the HP traffic are always the contracted ones,while no guarantee is given to the LP traffic. The latter couldbe an IP best effort or an ATM ABR traffic.

We envisage two ways of operation:Case a: deterministic QoS guarantees: at connection set-up,

the SaT requests the MCS to establish a connection with acapacity equal to C cells/s. The MCS accepts connection

requests until the sum of the relevant capacities is less thanor equal to the overall capacity of the involved links (i.e.with a peak allocation). Given the circuit switching transfermode of the ESW system, this means that the SaT requestsa circuit with capacity C. However the HP traffic usestransport resources only when they are effectively neededand the capacity actually used is then a function of time,C(t)≤C. The remaining capacity C- C(t) can be used by LPtraffic (belonging to the same SaT or to other SaTs). Thecapacity C is then shared between HP and LP traffic in adynamic way, as a consequence of IBRs. With thisapproach the HP traffic does not experience lossphenomena.

Case b: statistical QoS guarantees: it works as the abovesolution with the difference that the MCS does not exert apeak allocation but a statistical one; loss phenomena canoccur, but a suitable CAC assures that the performancemeasures perceived by the HP sources are always therequested ones.

uplink

Terminal or IWU

buffer &(W)

Control of the buffer contentand of the capacity assignment

MCS:CAC functions

Satellite:capacity assignment

6��

+3�VRXUFHV�RI�FODVV��

6.��

+3�VRXUFHV�RI�FODVV�M

6�M

R���W�

R.MM�W�

Exchange of signalling information

RLM�W� Traffic offered by the i-th HP source of class j

buffer &�&(W)/3�WUDIILF�VRXUFHV

%

&LP buffer

HP buffer

VLM�W� Traffic offered by the i-th HP source of class j,

once shaped by a DLB shaper

R�M�W�

R.���W�

�

�

�

�

DLB

DLB

DLB

DLB

�

�

V���W�

V.���W�

V�M�W�

V.MM�W�

6.MM

Figure 1: System Architecture of a generic SaT

The above solution regards the CAC operation of the MCS(denoted to in the following as "MCS related CAC rules"). It isclear that, in Case a above, these rules become the trivial peakallocation ones. The rules relevant to Case b will be insteaddiscussed in Section 5. However, the DBAC imply thenecessity of another set of functions and of rules, which can beconsidered as of pertinence of the SaT.

In particular, we have to foresee a methodology to choosethe values of the system parameters so that the HP usersperceive the desired performance. For instance, given Ksources, an HP buffer of size B and the TDs of each HP trafficsource, we might want to determine the value of theconnection capacity C such that the users requirements in lossand delay are satisfied. Inversely, given C, B and the TDs ofeach HP traffic source we could be interested in determiningthe value of K such that the users are pleased with theperceived performance, even in presence of the DBACmechanism (we stress that the latter takes away the bandwidth

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from the HP sources, when not needed, and it takes a roundtrip time to give it back). The former case is generally called adimensioning problem while the latter one is referred to asdefinition of CAC rules. For the sake of simplicity, in thefollowing we will generally speak of "SaT related CAC rules",being obvious that the same rules can be used both fordimensioning and for resource allocation purposes.

The DBAC has then a twofold application purpose:1. At MCS level, it improves the system efficiency by

allowing the allocation of a number of SaTs greater thanthe number that would be achieved by means of a peakallocation (in Case b above);

2. Once a SaT is assigned a given connection, the bandwidthmay be handled dynamically, without involving the MCS,so that also LP traffic can be delivered, and the channelutilisation factor improves further.

Finally, the possible statistical multiplexing of K sources onthe same ESW connection (Fig. 1) helps in increasing theoverall efficiency.

The SaT related CAC rules are an essential point of ourscheme. In fact, given the system latency ∆T, the HP trafficcan not immediately use the capacity that it needs. This meansthat the values of C, B and K must be suitably chosen, as afunction of the TDs of the HP traffic sources and of the delayand loss performance requested by the HP traffic. This appliesalso when a connection supports only one HP source. In fact, asingle HP source could experience loss and delay, even if thecapacity requested at connection set-up is equal to its PeakCell Rate, unless a suitable storage capacity is used and aproper CAC is exerted. This happens because the capacity ofthe connection is not always immediately available, owing tothe adopted DBAC scheme and to the system latency. Thisexplains why a SaT must always adhere to CAC rules.

Finally, we remark that we have distributed the CAC rulesbetween MCS and SaTs. A different solution could have beento implement also the SaT related rules in the MCS, thussimplifying the terminals. However, in this case, the“connection request” messages should contain also the TDs ofeach supported HP traffic source, the performance measuresrequested by each HP source and the size of the HP buffer ofeach SaT. This would make more complex the MCS andincrease the signalling traffic and the relevant delay.

Thanks to the significant simplification implied by theDLBs, the CAC problem becomes simpler. To define the SaTrelated CAC rules we start from the ones envisaged in [3 and10] and we suitably modify them. In [3] the Authors consider ageneric network element, composed by a statistical multiplexerwith a FIFO queue, fed by traffic sources regulated by meansof DLBs. With reference to such network element, they designsimple and effective CAC rules that allows guaranteeingQuality of Service (QoS) requirements in loss and delay.

In the following we will define the SaT related CAC rulesso as to avoid loss phenomena at the terminal (losslessmultiplexing). It is obvious that an alternative solution is toallow small losses at the SaT. This alternative is not discussedhere for space limitations. The main difference between oursystem and the one considered in [3] is that the server of the

HP traffic in our system goes on vacation according to a givenlaw (to be described in the following). In other words, the HPserver capacity is not constant but it varies dynamically as aconsequence of IBRs. To complete the definition of ourscheme we must describe how and when a SaT decides torequest more capacity to transport HP traffic or to release aportion of the capacity that it is has been using for the HPtraffic. In other words, we must define the law followed by theHP server to go on vacation. This will be done in the nextsection.

III. SAT RELATED CAC RULES

In this section we assume that the MCS CAC procedure hasassigned a given bandwidth, say C, to a connection in a givenSaT. Eventual modifications of the capacity actually used mayhappen in every frame, but, when the SaT asks for a bandwidthvariation, this variation is effective only when the TRMmodule on board the satellite acknowledges the request.

The algorithm used to dynamically assign capacity to theHP traffic of a given connection (and, as a consequence, to theLP traffic) is an important issue of our scheme. We assumethat the value of C(t), that is the capacity being used by the HPtraffic, is chosen as a function of the content of the HP buffer.The remaining capacity, C-C(t), is offered to the LP traffic. Itis clear that C(t) must be a non-decreasing function of the HPbuffer content: when the content of such buffer increases, theHP traffic requires more capacity and vice-versa. Weconsidered [5] different laws of variation of C(t), as a functionof the HP buffer occupancy, v(t).

The simplest of these laws, denoted as C(v), is shown in Fig.2. When v(t), (i.e. the HP buffer occupancy) is less than agiven threshold, denoted as v0, the capacity assigned to the HPtraffic is equal to a value denoted as Cmin; when v(t) is greateror equal to v0 then C(t)=C.

C

Cmin

Bv0Buffer content

Cap

acit

y as

ssig

ned

to

th

e H

P t

raff

ic

v

C(v)

Figure 2: Assignment of capacity to the HP traffic as afunction of the HP buffer occupancy

For comparison purposes, we define also a Referencesystem. Such system is a plain circuit switching one, withoutDBAC capabilities, where the bandwidth assigned to each SaTis constant. Also in such system we foresee a buffer of size B,where several HP sources can be statistically multiplexed onthe same connection, by using the multiplexing rules defined in[3]. The Reference system is then a system where each ESWconnection transports only the HP traffic. The server thatmodels the connection capacity of the Reference system does

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not go on vacation and it must be constantly available totransport HP traffic, i.e. ( ) W��&� W& ∀ .

The mean value of the capacity used by our system todeliver HP traffic is less than that of the Reference system. Ifwe want the HP traffic to perceive the same loss performance(i.e. zero loss) of the Reference system, it is necessary that asuitable amount of buffer space, ∆B, be dedicated to thecompensation of the lower value of the average capacity and ofthe system latency. Such buffer space, ∆B, may be added to Band, in this case, we can allocate the same number of HPsources as in the Reference system. Otherwise, ∆B may beseen as a part of the overall buffer size B. In the latter case,the buffer that remains to handle the “pure” multiplexing of theHP sources is lower (B-∆B), therefore less HP sources (∆K)can be supported than in the Reference system. The parameter∆B will be referred to as ∆BOUT, when added to B and as ∆BIN,when considered as a part of B.

To evaluate ∆B we assume that all the HP sources belong tothe same class (homogeneous sources) and are characterisedby the same values of their TDs (PS, rS and BTS). We consider asingle ESW connection in a given SaT. The following resultscan be extended to the heterogeneous sources case.We establish the following notations:- B: the HP buffer size (in cells);- v(t): the HP buffer occupancy, at the time t (in cells);- C: the overall capacity allocated to the considered

connection (in cells/s);- K: the number of HP sources supported by the

considered connection in the considered SaT.- C(t): the capacity used, at the time t, by the HP traffic

belonging to the considered connection;- ∆T: the delay for putting into effect the capacity

assignment command, mainly due to the round triptime of the satellite link (in seconds);

- ρTOT: the total utilisation factor of the consideredconnection.

Let us now consider a generic function C(v). We assume thetoken buffer of the shapers to be full at the initial time of abusy period, ti. During the busy period, if K DLB regulated HPsources are emitting traffic at the peak rate Ps, the followingrelation applies:

( )( ) ( )( )VV

76 LV

U3

%WWW����7WY&.3

GW

WYG

−=≤≤∆−−= (1)

Without loss of generality we may assume ti=0. Thesolution of the above differential equation allows determining

∆B. In fact, by integrating (1) in the interval ]0[ WW� ≤ we

obtain:

( ) ( )( )∫ ∆−−=W

V GW7WY&W.3WY0

(2)

Since KPs>C, the maximum of v(t) is reached for t=t*:

( ) ( )( )∫ ∆−−=

W

V GW7WY&W.3WY

0

(3)

If all the capacity C were always available to the HP traffic,as in the Reference system, we would obtain:

( ) ( ) V

F W�&.3WY −= (4)

Instead, our system needs an additional buffer space, withrespect to the Reference system; this additional buffer space isequal to:

( ) ( ) ( )( )∫ ∆−−=−=∆

W

F GW7WY&&WWYWY%

0

(5)

The above relation shows that the value of ∆B depends, bymeans of an integral relation, on the capacity assignment law,C(v). Therefore we must choose a specific law in order toevaluate ∆B and to define the CAC rules. However, it can beshown that, by choosing suitably the parameters of one specificlaw (e.g. the one shown in Fig. 2), it is possible to obtain thesame value of ∆B implied by whatever other law one maychoose. In fact, if we are willing to use a compensation bufferspace of size equal to a value ∆B, then the only requirementthat we have to satisfy is that the mean value of C(t) in theinterval [0, t*] is:

( )( ) ( )

W

W

W

W

%&

W

GWW&

W

GW7WY&

&

∆−==

∆−

=∫∫00 (6)

The condition (6) can be satisfied by an appropriate choiceof the parameters of the assumed law of capacity assignment(i.e. v0 and Cmin). This result derives from (5) and can be furtherclarified by Fig. 3, which shows, as a shaded area, a graphicalinterpretation of the quantity ∆B, for a generic law of capacityassignment.

&

W

&�Y�W���∆7��

∆B

7LPH&DS

DFLW\�DVVLJQHG

WR�WKH�+3�WUDIILF

Figure 3: Graphic interpretation of the quantity ∆B

All this means that, as far as the value of size of ∆B isconcerned, we can restrict ourselves to use always the samecapacity assignment law (the one shown in Fig. 2), withoutloss of generality. We are now interested to see if the sameproperty applies also to other system parameters, such as:� the number of acceptable HP sources, K;� the maximum delay perceived by the HP users in the HP

buffer, DMAX.If that were the case, we could avoid considering different

laws of capacity assignment. In the following, we will refer tosuch property as to the Law Independence property, or LIproperty. We have seen that the LI property applies to ∆B. Wenow check if the LI property applies also to the number of

0-7803-5883-X/00/$10.00 (c) 2000 IEEE IEEE INFOCOM 2000

acceptable HP sources, K. To this end we have to distinguish ifour system and the Reference system have the same buffer sizeor not. Let us consider the first case. The quantity ∆B is a partof the overall buffer size B. A connection with capacity C cansupport less HP sources than in the Reference system (∆K) andthe parameter ∆B will be referred to as ∆BIN.

Let c and b denote the effective bandwidth and bufferallocation, respectively, of the HP sources [3]. In this case:

.E%%F�& ,1 =∆−= )/( (7)

Since we want to avoid loss phenomena at the HP buffer,the following relation must hold [3]:

E%U3

F376

VV

V =−−

(8)

From (7) and (8) we obtain:

( ) ,1

V %%W&.3 ∆−=− (9)

Equation (9) shows the dependence of K on ∆BIN and provesthat the LI property applies also to K, since it applies to ∆BIN,when the compared systems have the same overall buffer size.When ∆B is added to B (i.e. ∆B=∆BOUT) both systems supportthe same number of HP sources, K. In this case, it is evidentthat K does not depend on the capacity assignment law.Therefore we can conclude that the LI property applies to K.

The LI property does not apply, in general, to the maximumdelay, DMAX. However, if a given requirement on DMAX can besatisfied by adopting the chosen law, then, given its simplicityand the fact that the LI property applies to all the remainingperformance measures of interest, we can always adopt suchlaw, without loss of generality. On the other side, we verifiedthat this law can satisfy a wide range of values of DMAX. Forthese reasons, in the remainder of this paper, we consider onlythe above capacity assignment law. Thanks to such assumptionwe can first particularise the relations given above and thendesign the SaT related CAC rules. By expressing the aboveequations as a function of the parameters of the assumed lawof capacity assignment (i.e. v0 and Cmin) we get:

( ) ( )( ) ( )( )

( )( )

≤<∆+∆−−−+

+∆+−=∆+≤≤−=

V

PLQV

PLQV

WW7W����7WW&.3�����

7W&.3WY

7WW������W&.3WY

00

0

0

(10)

where )(00 PLQV &.3�YW −= is the first time when the

threshold v0 is reached.By combining (5) and (10) we have:

( ) ( ) ( )( )

( )

∆+

−−

=∆+−=−=∆

7&.3

Y�&&

7W&&WYWY%

PLQVPLQ

PLQ

F

0

0

. (11)

Fig. 4 shows a graphic representation of the compensationbuffer size, ∆B; in this figure the curves v1(t) and v2(t) aregiven by:

( ) ( ) V WW������W&.3WY ≤≤−=1 (12)

( ) ( )( ) ( )

( )( )

≤<−−+

+−=≤≤−=

V

PLQV

PLQV

WWW�����WW&.3�����

W&.3WY

WW������W&.3WY

11

12

12

for

for

(13)

where 7WW ∆+= 01 , and t* is defined in (1).

∆B

Y�W�

W

Y�

∆7

Y��W�

Y��W�

W� W� W 7LPH

%XIIHU�FRQWHQW

Figure 4: Graphic representation of ∆B

With these results, we can derive the SaT related rules,starting from the case of ∆B=∆BIN. To this aim, we mustdetermine the unknown quantities c, b, K, and ∆BIN, by meansof the following system of equations (which collects (7), (8),and (11)):

( )

=

∆−=

=−−

∆+

−−=∆

.F&

E

%%

F&

E%U3

F3

7&.3

Y�&&%

,1

76VV

V

PLQVPLQ,1

0

(14)

This non-linear system is relatively easy to solve. However,we must check the physical acceptability of the mathematicalsolutions provided by (14). The solutions are physicallyacceptable if ∆B<B and rs≤c≤Ps. We also assume that ρTOT<1.

Following the approach of [3], the solution of the abovesystem may be graphically represented as shown in Fig. 5.

The following considerations are in order.� The maximum number of HP sources that can be accepted,

K, is a number belonging to a range I contained in theinterval [C/P, C/rs]; such range I is a function of the systemparameters and decreases when ∆BIN increases;

� When the threshold v0 increases and Cmin decreases, thevalue of ∆BIN increases, the effective bandwidth tends to Ps

and the corresponding effective buffer vanishes. Thismeans that B=∆BIN. The entire HP buffer is used tocompensate the lower value of the mean value of thecapacity usable by the HP traffic and the system latency.There is no buffer available for multiplexing purposes. Thisalso implies that the capacity Cmin can not be lower than a

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suitable bound, which depends on the value of the thresholdv0, otherwise we would obtain unacceptable solutions fromthe system of equations (14), that is

7�Y%&&PLQ ∆−−≥ )( 0 (15)

E

F3V

E%%

F&

,1∆−=E%

U3F3

76

VV

V =−−

UV

F�

E�

%76

(IIHFWLYH�EDQGZLGWK

(IIHF

WLYH

�EXIIHU

Figure 5: Determination of effective bandwidth and effectivebuffer for lossless multiplexing

Let us now consider the case ∆B=∆BOUT. The total buffersize is BTOT=B+∆BOUT. In this case, we can allocate the samenumber of HP sources, K, as in the Reference system. Thenumber K can be obtained by solving the system of equations:

=

=

=−−

.F&

E%

F&

E%U3

F376

VV

V

(16)

The corresponding overall buffer size is given by:

( )

∆+

−−+= 7

&.3Y

�&&%�%PLQV

PLQ7270 (17)

The above rules guarantee that our system and theReference one have the same loss performance (zero loss). Ifwe want that also the maximum delay suffered by the HPtraffic be equal in both system we must add a furtherconstraint. We conclude then this Section with the definition ofrules including such constraint. Since the maximum delay mustbe not greater than that suffered in the Reference system, thecompensation buffer space, ∆B, must be included in B,therefore the parameter ∆B will be referred to as ∆BIN. Inaddition, the average capacity used by the HP traffic is smallerthan that of the Reference system and less than C. This meansthat the size of the overall buffer size of our system must besmaller than that of the Reference system. The value of B mustthen be determined by using a suitable constraint, which mustbe added to those of (14). The set of unknown quantities of theresulting system of equations is therefore given by c, b, K,

∆BIN, and B. To determine the additional relation that gives thedesired value of B, we start by recognising that the maximumdelay, Dmax, is equal to the delay suffered by the last cell in afull HP buffer.

This delay is composed of two contributions:1. a period lasting 7&�Y% ∆+− )( 0 , during which the buffer

is emptied at a rate C;2. a period lasting PLQ&�7&Y )( 0 ∆− , during which the

buffer is emptied at a rate Cmin.The additional relation is then:

7&�Y% ∆+− )( 0 + PD[PLQ '&�7&Y =∆− )( 0 (18)

Finally, we remark that, if &�Y7 0≥∆ , the maximum

delay is equal to that of the Reference system (and the secondcontribution above is equal to zero).

IV. SAT RELATED CAC RULES PERFORMANCE

A comprehensive presentation of the performance of theSaT related CAC rules can be found in [5]. In this section wepresent only the main results, by focusing on the capacitymade available to carry LP traffic and on the total utilisationfactor of the considered connection, ρTOT (i.e. the utilisationderiving from the superposition of HP and LP traffic). It isworth stressing that we evaluate the capacity that the LP trafficcan potentially use and not the one effectively used. Thedifference between these two quantities depends on the LPtraffic generation characteristics and on the LP buffer size.

The capacity made available to carry LP traffic depends onthe output processes of the DLB regulators and these, in turn,depend on their input processes, that is to say on the statisticalproperties of the sources loading the DLBs. This means thateach particular kind of source feeding the DLB gives rise todifferent performance measures of our system. Instead ofevaluating the system performance by assuming specific kindsof sources, we will determine upper and lower bounds of theabove performance measures. Such bounds do not depend onthe particular sources feeding the DLBs.

We consider two extremal behaviours of the output processof a generic DLB. The first one, is a DLB that emits cells at aconstant rate equal to the Sustainable Rate, rs. The second oneis a DLB that emits cells according to an ON-OFF process; inthe ON state, it transmits cells at a rate Ps; in the OFF state itdoes not transmit. The length of the ON and OFF periods aresuch that the overall mean rate is equal to rs. We conjecturethat the first behaviour results in the best possibleperformance, as far as the capacity made available to carry LPtraffic is concerned, while the second behaviour gives rise tothe worst possible performance. Accordingly, the parametersrelevant to these two behaviours will be labelled with BESTand WORST, respectively. In both these cases we willevaluate ρTOT as a function of the parameters of the assumedcapacity assignment law (v0 and Cmin). In [5] we show that:

>+−

≤=ρ

VPLQVPLQ

VPLQ

%(67�727.U&���������

&

.U&&

.U&����������������������������������

for

for1(19a)

0-7803-5883-X/00/$10.00 (c) 2000 IEEE IEEE INFOCOM 2000

&

&�

%

'�U

3

U3 PLQ

76

0$;V

V

VV:2567�727

−

−−=ρ 11 (19b)

&�Y7 0for ≤∆ , while

( )

−−∆

−−=ρ

&

&��W&�Y7

3%

U3U PLQ

V76

VVV:2567�727 01 (19c)

&�Y7 0for >∆ ,

where 0$;' is given by (18) and

7&Y%

U3

U3%

WV

V

VV

76 ∆−−−

−

−= 01

In the WORST case, the system is stable only if:

&

Y%7

U

3

U3

%

7&Y&

V

V

VV

76

PLQ

0

0

1−

−∆−

−

−

∆−≥ (20)

Fig. 6 shows the upper (BEST) and lower (WORST) boundsof ρTOT as a function of Cmin/C when ∆B=∆BIN; the lossperformance and maximum delay are identical to those of theReference system (Eqs. 14 and 18). For comparing theproposed approach to the Reference system, a solid linecorresponding to the utilisation factor of the Reference systemis plotted, and labelled “(no DBA)”.

The values of the system parameters are:� Ps=32000/(48 X 8)=83.33 cells/s;� rs= 32.197 cells/s;� BTS=100 cells;� C=2 048 000 / (53 X 8)= 4830. 189 cells/s;� ∆T=0.25 s.

0.45

0.55

0.65

0.75

0.85

0.95

1.05

0 0.2 0.4 0.6 0.8 1&PLQ�&

8WLOLVDWLRQ�IDFWRU

BEST ( vo=0.5 B )

WORST ( vo=0.5 B )

( no DBA )

K=59; B=2522

K=76; B=3000

K=70; B=2940

K=66; B=2867

K=63; B=2756

K=63; B=2756

K=59; B=2522

K=66; B=2867

K=70; B=2940

.12�'%$� ���

%12�'%$� ������

Figure 6: Overall utilisation factor of the consideredconnection, as a function of Cmin/C

As the ratio Cmin/C varies, so does the number of HP sourcesthat can be allocated in our system (K) and the value of thebuffer size (B) needed to avoid loss phenomena in our system.The Reference system can support 76 sources (KNO_DBA=76) andits buffer size is equal to 3000 cells (BNO_DBA=3000). Adimensioning criterion that resulted from the analysis is that anoptimal working point corresponds to selecting a value of Cmin

equal to Krs; in fact, this choice produces a full utilisation

factor and the maximum number of HP sources allocated.Should this be not possible, due to boundaries (15) or (20), thevalue of Cmin should be the closest to Krs that satisfies suchconstraints. In Fig. 6, the optimal working point corresponds toCmin/C equal to about 0.42.

We can observe that:� the proposed approach results in a marked increase of the

overall utilisation, with respect to the Reference system;this improvement increases when the traffic burstiness (i.e.the ratio Ps/rs) increases;

� the price to be paid for such advantage is a reduction of theHP sources, which is compensated by the possibility totransport LP traffic. Note also that our approach uses asmaller buffer size (so as to provide the same maximumdelay of the Reference system); if the HP traffic couldtolerate a higher delay we could support the same numberof HP sources while increasing the overall utilisation factor(case of ∆B=∆BOUT);

� the capacity made available to the LP traffic tends todecrease when Cmin increases, while the number K ofallowed HP sources increases;

� when the value of Cmin approaches C, the number of HPsources tends to that of the Reference system, since theDBAC mechanism tends to have no effect;

Other results, including those relevant to the case ∆B=∆BOUT

and to single sources, can be found in [5].

V. MCS RELATED CAC RULES

As said in Sec. II, the MCS related CAC rules can bedefined according to two approaches: peak allocation (and nocell loss) or statistical one with small loss probabilitiesallowed. The first one is trivial: the maximum number of SaTsthat can access simultaneously a link with capacity 7& is:

&�&+ 7/26612 = (21)

In this case, the only way to increase the link utilisation,with respect to the Reference system, consists in using theDBAC, which allow transporting also LP traffic.

Let us now consider the second approach (statisticalallocation). We first assume that all the SaTs have the samecharacteristics (homogeneous terminals) and then we willextend the results to the heterogeneous case. In any case, weassume that the traffic loading the generic SaT is independentby that of the others terminals.

A.� Homogeneous terminalsIn order to derive the CAC rules a first (conservative)

solution is to assume a worst case behaviour of the outputprocess of the SaT: each SaT alternates between the twoemission rates PLQ& and C, (Fig. 7).

In a time period V

V U�W37 = , the maximum capacity C is

requested for a time [7 given by:

+

−−+=

&&.3Y

&%

W7PLQ

[

110 (22)

During the period [77 − , the capacity used is PLQ& . We

0-7803-5883-X/00/$10.00 (c) 2000 IEEE IEEE INFOCOM 2000

now assume that the phase displacements of the aboveemission processes, relevant to all the involved terminals, areuniformly distributed. The assumption to consider all theemission processes synchronised would be too pejorative. Wenow let:- �W�&�W�& LL ϑ−= : the instantaneous capacity requested by

the i-th SaT, where Lϑ is uniformly distributed in

[ )7�0 ;

- U(t): the total instantaneous capacity requested by all theSaTs;

- ORVV3 : the loss probability suffered by the HP traffic;

- H: the number of SaTs that can be accepted by theMCS in a link with a total capacity equal to 7& ,

under the requirement that ORVV3 be less than a

given threshold, L.

7[

W7

&

&PLQ

&�W�

7LPH

%DQGZLGWK�GHPDQG

Figure 7: Worst case capacity request from a single SaT

The value of H must satisfy the following inequality:

( )

/&�W�&3U

&�W�&3U&�W�83U3

7

+

L

L

7

+

L

L7ORVV

≤

>=

=

>ϑ−=>=

∑

∑

=

=

1

1(23)

The last relation in (23) is maximised [3] by the probability

that the sum of the H random variables L&Ö (where L&Ö is the

random variable relevant to �W�&L ) exceeds the value 7& ; the

p.d.f. of L&Ö is:

( ) ( ) ( )&&Ö�7

7&&Ö

7

7&ÖS L

[PLQL

[L −δ+−δ

−= 1 (24)

where δ is the Dirac function.An alternative to the worst case behaviour of Fig. 7, which

results in a less conservative allocation, is to assume thatwhenever the HP buffer content exceeds the threshold 0Y , the

SaT emits at the rate C for a time period equal to [7 (22), as in

the worst case. In this case the probability that the threshold

0Y is exceeded is taken into consideration and (24) becomes:

( ) ( ) ( ) ( )PLQLLL &&Ö���&&Ö�&ÖS −δω+−δω= , (25)

where ( )�[ YY�W�3U�77 >=ω and ( )�YY�W�3U > is derived in the

Appendix.To satisfy the bound in relation (23), we use the sum of the

random variables L&Ö instead of the stochastic process U(t) and

we evaluate an upper limit of ORVV3 by means of the Chernoff’s

bound. According to this approach, we must define the

moment generating functions for L&Ö , given by:

( ) V&V&&ÖV HH@H>(�V�0 PLQL ω+ω−== 1 . (26)

We assume that the stability condition [3] is verified:

[ ] 7

+

LL &&Ö( <∑

=1(27)

and that loss phenomena can occur:

7V

&�V�0�V�0

�+OLP >∞→

(28)

With this position, for s>0, relation (23) becomes:

)( 1

1

7

+

L

L V&&ÖV

7

+

LLORVV HH3U&&Ö3U3 >=

>≈

∑

=

=∑ . (29)

and, by using relations (26) and (29), an upper bound of

ORVV3 is given by (Chernoff’s bound):

+V&&ÖV

V&ORVV �V�0HH(H3 7

+

L

L

7 −∑− =≤ = ][ 1 (30)

We can make this bound tighter by minimising the functionin the variable s on the right-hand side; this can be done bymaximising the function F(s) defined as [3]:

( )�V�0ORJ�+V&�V�) 7 −= (31)

This function has a single maximum V >0, given by:

−

−ω−

ω−

−=PLQ7

7

PLQ

+&&&+&

ORJ�&&�

V1

1(32)

We can now use the large deviation approximation toChernoff’s bound, where ORVV3 is approximated by the

following expression [3]:

( )πσ

≈−

2�V�V

H3

V)

ORVV

(33)

and �V�2σ is [3]:

−=σ2

2�V�0�V�0

�V�0�V�0

+�V� (34)

Finally, H can be found by solving the following equation:

( )/

�V�V

H

V)

=πσ

−

2(35)

The effective bandwidth for each SaT is therefore given by:

+�&& 7= (36)

where & is bounded by ( )PLQPLQ &&& −ω+ and C.

0-7803-5883-X/00/$10.00 (c) 2000 IEEE IEEE INFOCOM 2000

B.� Heterogeneous terminalsThis case is deeply discussed in its general form in [3]. It is

necessary to consider the superposition of a plurality ofstochastic process �W�8 M that represents the bandwidth

demand of each class of terminals ( 1���M 1= ). The treatment

is analogous to that of the homogenous case, with the presence

of different kind of random variables ML&Ö used to represent

the different bandwidth demand of the N types of terminals. Ifthe maximum cell loss probability tolerated is L, the solutionof the problem is the set }{ 1�����M��+M+ == that satisfies the

following inequality in the tightest way:

/&�W�&3U&�W�83U3 7

1

M

+

LML7

1

MMORVV

M

≤

>=

>= ∑ ∑∑

= == 1 11

.

(37)

Also in this case we can use the Chernoff’s bound with thefollowing formalism:

( ) ( ) ( )MMLMM

PLQMLM

ML &&Ö&&Ö��&ÖS −δω+

−δω= (38)

where

>=ω M�

M

M

M[M Y�W�Y3U�

7

7 and the derivation can

continue as in the case of homogeneous terminals [3,5].

VI. NUMERICAL RESULTS

In this section we present some results with the aim ofvalidating the approximation of the threshold crossingprobability presented in the Appendix and of evaluating theperformance of the proposed approach. The values of thesystem parameters are equal to those of Sec. IV, with theexception of the total link capacity, 7& , which is now equal to

45 Mbit/s. Fig. 8 shows the analytical upper bound and somesimulated values of the threshold crossing probability,

( )0Y�W�Y3U > , as a function of the HP buffer size and for

different values of the ratio %�Y0 . The value of Cmin is the

smallest possible value greater than the optimal working pointKrs (note that the bandwidth in our system is quantised withsteps equal to the basic channel). The figure confirms that thederivation presented in the Appendix gives an upper bound of

( )0Y�W�Y3U > and allows evaluating its tightness.

Fig. 9 shows the number of SaTs that can be allocated as afunction of the required loss probability, L, and for differentvalues of B and of the ratio %�Y0 .

We observe that:1. when %�Y0 increases, the threshold crossing probability

decreases and then, for a given buffer value, the averagecapacity demand from each SaT is sensibly lower;

2. when B increases, the dependence of H from the lossprobability becomes less evident; this phenomenon is dueto the lower values of threshold crossing probability,which tends to make the increase of H slower. In fact, wemust remember that the average bandwidth demand islimited by C and �&&�& PLQPLQ −ω+ , - see comment

after (36) - so that when ω is very small, the capacityallocation is always close to PLQ& .

3. the number of SaTs, H, with lower buffer space (B=2000)can be higher than the one with more buffer space(B=5000) (for %�Y 500 = in this figure). This is because

each SaT may support a variable number of traffic sourcesand it may happen that, when we have a lower number ofSaTs we also have a higher number of traffic sourcessupported by such SaTs (and viceversa). However, theoverall supported HP traffic (i. e. the number of HPsources, K) is always a non-decreasing function of thebuffer size (as it must be). In any case, a marked increaseof H, with respect to the value relevant to the peakallocation ( /26612+ ), is always evident.

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1000 2000 3000 4000 5000 6000 7000%XIIHU�VL]H��FHOOV�

7KU

HVKR

OG�FURVVLQJ�SU

REDE

LOLW\

v0/B = 0.3 Mod v0/B = 0.5 Modv0/B = 0.3 Sim v0/B = 0.5 Sim

Figure 8: Threshold-crossing probability vs. buffer size

15

20

25

30

35

40

45

50

1.E-11 1.E-09 1.E-07 1.E-05 1.E-03 1.E-01&HOO�ORVV�SUREDELOLW\

1XP

EHU�RI�WHUPLQDOV

B=2000, v0=0.3 B B=2000, v0=0.5 B

B=5000, v0=0.3 B B=5000, v0=0.5 B

HNO LOSS = 21

Figure 9: Number of terminal vs. cell loss probability

A last consideration is the following. When a capacityrequest from a SaT is denied, the corresponding cell loss is notdistributed among all the SaTs, but affects only the involvedterminal (this loss is likely to be distributed among the users ofthat terminal, if more than one user is supported). However,thanks to the HP buffer, the SaT begins to loose cells only afterhaving filled its HP buffer. In fact the latter is not necessarily

0-7803-5883-X/00/$10.00 (c) 2000 IEEE IEEE INFOCOM 2000

full when a capacity request is denied by the TRM and so theeffective cell loss suffered by that SaT is less than theestimated one. This is because ORVV3 has been evaluated as the

fraction of time in which there is not sufficient link capacity.An evaluation of the overall efficiency factor resulting fromthe joint application of SaT and MCS (statistical) related CACrules can be found in [5].

VII. CONCLUSIONS

In this work we have shown that it is possible to improvesignificantly the efficiency of a circuit switched satellitesystem by means of the DBAC and in particular that it ispossible:� to use efficiently the bandwidth assigned to each SaT by

releasing a portion of it to the LP traffic;� to allocate a number of SaTs greater than that relevant to a

peak allocation. In this way, even if the bandwidthavailable for the LP traffic is reduced, the number of HPusers increases considerably;

� to increase the connection carrying capacity for givenbuffer spaces by allowing small cell losses in the HPbuffers; this result is not shown here for space limitations.

� to provide QoS guarantees for the HP traffic.In future work we propose to enhance our approach in

several respects. First, we intend to study the performanceperceived by the LP traffic, in terms of loss and delay. Second,we want to integrate in our framework a reactive controlscheme, to guarantee the requirements in loss of the LP traffic[e.g. 8]. Third we want to improve the approximation in theevaluation presented in the Appendix.

APPENDIX

An upper bound of the ( )0Y�W�Y3U > can be evaluated by

solving a queuing system that models an HP buffer loaded by asuperposition of K WORST case DLBs output processes (thatis, deterministic On-Off sources, with an On period consisting

of a burst of fixed length equal to V 3WD = cells) with random

relative phasing. The service time alternates between thevalues relevant to the output rates C and PLQ& . To solve this

system we make some approximations: i) we assume aninfinite buffer size (which is a conservative assumption, in ourcase); ii) we assume that the output rate is always constant andequal to PLQ& ; this allows avoiding the complexity resulting

by a service time that is a function of the buffer content. Notethat this implies that the value of PLQ& can not be smaller than

Krs, so that the queue utilisation factor is less than 1; (note alsothat, for values of Cmin near to the optimal working point Krs,the Chernoff’s bound approach gives for ( )0Y�W�Y3U > values

very near to one); iii) we approximate the arrivals of all thecells of a burst with an instantaneous aggregated arrival ofequivalent size. The latter assumption is made since the exactsolution of the queuing system up to now defined and with theabove two assumptions (available e.g. in [9]) has a highcomputational cost. We then normalise all the variables withrespect to the burst size a, so that we can apply the results

obtained in [6] relevant to a 1�'�'. ⋅ queue, that is aqueuing model where each of the K sources generates just onecell in every period D with D (period normalised to the service

time) �W�Y (buffer level) and 0Y (threshold) defined as:

==

=

D�YYD��W�Y�W�YD�7&' PLQ

00

(39)

Under these hypotheses, the threshold crossing probabilitybecomes [6]:

( ) ( )

V'Y.'

'V

'V

VY

.

Y�W�Y3UY�W�Y3U

VY.VYY.

V−

+−

−

+

=

=>≈>

−−+−

=∑ 0

1 0

00

0001

(40)

REFERENCES

[1] G. Losquadro, V. Podda, F. Carducci: “TheEuroSkyWay Wordldwide system providing broadbandservice to fixed and mobile end-users”, 4th KA bandUtilization Conference, Venezia, Italy, 2-4 Nov. ’98.

[2] ATM Forum, "Traffic Management Specification",v4.0.

[3] A. Elwalid, D. Mitra: “Traffic shaping at a networknode: theory, optimum design, admission control”,IEEE Infocom 97, pp. 445-455.

[4] ITU-T Recommendation I.371, "Traffic control andcongestion control in B-ISDN".

[5] N. Blefari-Melazzi and G. Reali: “A ResourceManagement Scheme for Satellite Networks withDynamic Bandwidth Allocation Procedures”, TechnicalReport, University of Perugia, available on request(blefari@diei.unipg.it).

[6] J. W. Roberts, J. T. Virtamo: "The superposition ofperiodic cell arrival streams in an ATM multiplexer";IEEE Transactions on Communications, Vol. 39, No; 2,February 1991, pp. 298-302.

[7] Mertzanis, G. Sfikas, R. Tafazolli, B. G. Evans:“Protocol Architecture for Satellite ATM broadbandNetworks, Communications Magazine, March ’99, pp.46-54.

[8] A. Baiocchi, N. Blefari-Melazzi, M. Listanti, C.Soprano: “Definition and performance analysis of asimple, ABR-like, congestion control scheme forsatellite ATM networks with guaranteed lossperformance”, IEEE JSAC, Vol. 17, N. 2, February1999, pp. 303-313.

[9] A. Baiocchi, N. Blefari-Melazzi, F. Cuomo, M.Listanti: "Circuit Emulation Approach to TrafficControl in a B-ISDN", Computer Communications,Elsevier, Vol. 20, Issue N.1, January 1997, pp 11-28.

[10] A. Elwalid, D. Mitra, R.H. Wentworth: “A NewApproach for Allocating Buffers and Bandwidth toHeterogeneous, Regulated Traffic in an ATM Node”,IEEE J.S.A.C. Vol. 13, N. 9, August 1995, pp. 1115-1127.

0-7803-5883-X/00/$10.00 (c) 2000 IEEE IEEE INFOCOM 2000