156 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 1, NO. 1, JANUARY 2002

Performance Analysis of a PRMA Protocol Suitablefor Voice and Data Transmissions in Low Earth Orbit

Mobile Satellite SystemsGiuliano Benelli, Romano Fantacci, Senior Member, IEEE, Giovanni Giambene, and Carlo Ortolani

Abstract—Mobile satellite systems(MSSs) are expected to playa significant role in providing users with communication servicesworldwide. In such context, low earth orbit (LEO) satellite con-stellations seem to be a good solution to attain a global coverageand to allow the use of low-power lightweight mobile terminals.This paper analyzes the performance of a novel medium accesscontrol (MAC) scheme suitable for applications in LEO-MSSs,named Packet Reservation Multiple Access with Hindering States(PRMA-HS), that has been derived by proper modifications ofthe well-known PRMA protocol. We envisage a mixed traffic withvoice sources and data sources with different quality of service(QoS) requirements. The good behavior of the proposed PRMA-HSscheme is validated by extensive comparisons with the classicalPRMA protocol. Finally, it is shown here that PRMA-HS efficientlysupports integrated voice and data traffics in LEO-MSSs.

Index Terms—Mobile satellite systems, multiple access, networkarchitectures and protocols.

I. INTRODUCTION

FUTURE global-coverage mobile networks will integrate aterrestrial cellular segment and a satellite one partly (or to-

tally) based onlow earth orbit-mobile satellite systems(LEO-MSSs) [1]–[3]. This paper focuses onmedium access control(MAC) protocols and proposes a modification to thePacketReservation Multiple Access(PRMA) scheme to support bothvoice and data traffics in LEO-MSSs. Since satellites are powerand bandwidth limited, their resources must be efficiently ex-ploited. Hence, a voice terminal must transmit only during atalkspurt, by means of an activity detection scheme, so that vari-able bit-rate traffic is produced. Moreover, in order to increasethe resource exploitation of future MSSs, it is crucial that thebandwidth unused by voice traffic be assigned to data trafficsthat have not stringent delay requirements (e.g., traffics pro-duced by e-mail and Web browsing applications) [4]. Therefore,in our satellite scenario, the isochronous voice traffic well fitsthereal-time variable bit rate(rt-VBR) class, whereas the datatraffic is of theavailable bit rate(ABR) type [5].

Manuscript received June 4, 2000; revised November 5, 2000; acceptedNovember 5, 2000. The editor coordinating the review of this paper andapproving it for publication is W. Lu. This work was supported by the ItalianNational Consortium for Telecommunications (CNIT).

G. Benelli and G. Giambene are with the Dipartimento di Ingegneria dell’In-formazione—Università degli Studi di Siena, Via Roma, 56-53100 Siena, Italy.

R. Fantacci is with the Dipartimento di Elettronica e Telecomunicazioni—Università degli Studi di Firenze, Via S. Marta, 3-50139 Firenze, Italy.

C. Ortolani is with the Telecom Italia S. p. A., Unità Territoriale ClientiTop/Progettazione, Viale A. Guidoni, 42-50127 Firenze, Italy.

Publisher Item Identifier S 1536-1276(02)00193-9.

The PRMA scheme is based ontime-division multiple ac-cess(TDMA) and combines random access with slot reserva-tion [6], [7]. With PRMA, a voice terminal transmits its packetson a reserved slot only during a talkspurt. When a new talkspurtstarts, the terminal uses apermission probabilityscheme [7] toattempt transmissions. In terrestrial microcellular systems, theterminal promptly receives the outcome of an attempt (feedbackchannel), since theround trip propagation delay(RTD) is muchlower than the packet transmission time [7]. This is not true inLEO-MSSs, where RTD ranges from 5 to 40 ms, dependingon the satellite constellation altitude and the minimum eleva-tion angle. If the access packet experiences a collision (we ne-glect the capture effect [7]), the terminal knows only after RTDthat it must reschedule a new attempt. This delay significantlyreduces the PRMA efficiency in managing rt-VBR traffics inLEO-MSSs [8], [9]. We propose here a modified PRMA pro-tocol, where a terminal may attempt transmissions also whileit is waiting for the outcome of a previous attempt. If that at-tempt has been unsuccessful, a faster access is achieved. Other-wise, further attempts are useless and may hinder the accesses ofother terminals. Hence, this scheme has been calledPRMA withhindering states(PRMA-HS). We consider voice terminals(VTs) and data terminals(DTs) per PRMA-HS carrier in acell that use distinct permission probabilities (different servicepriorities). Eachuser terminal(UT), i.e., a VT or a DT, has abuffer to store packets to be transmitted.

II. TRAFFIC SOURCEMODELS

This section describes the adopted traffic models for both VTsand DTs. In the following, we denote by the frame duration,by the channel transmission bit-rate and by the voicesource bit-rate.

A. Voice Source Model

Each VT uses aspeech activity detector(SAD); talkspurtsand silent phases are assumed exponentially distributed withmean values s and s, respectively [7]. Thevoice activity factor is . An ac-tive VT generates one packet per frame. Each packet encom-passes informationbitsand headerbits. Thereare slots/frame, where is thefloor function and the slot duration is . The VTbehavior is described by: the probability that a silent gap endsin , ; the probability that a talkspurt ends during, ;

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BENELLI et al.: PERFORMANCE ANALYSIS OF A PRMA PROTOCOL 157

the probability that a talkspurt ends within , . Their ex-pressions can be found in [7], where they are respectively de-noted by , , . The first packet in the VT buffer is discardedif its transmission delay exceeds a specified maximum value,

; typically, ms [7]. When a packet is dis-carded, the VT tries to obtain a reservation with the next packet.Let denote the packet dropping probability for a VT; itis required for an acceptable speech quality. Thevoice throughput is pkts/slot.

B. Data Traffic Source Models

Two different DT traffic models have been considered: aPoisson traffic [10] and a WWW browsing one [11], [12]. Weassume that the packets of a message arrive simultaneously andsynchronized with slot times. Let denote the meanmessage length inpackets(bits, information part). We have

bitsmsg

(1)

The DT performance parameter is measured by the average mes-sage delay, , i.e., the mean time from the message arrivalto the DT buffer to the instant when this message is completelysent.

In the Poisson traffic case each DT (i.e., aPoisson DT) gen-erates messages independently of other DTs and according toa Poisson arrival process with mean ratemsgs/s. Assuming

, we can neglect the possibility that a Poisson DT pro-duces more than one message per slot. Hence, a DT generatesone message in a slot with probability . The messagelength in packets, , is geometrically distributed with expectedvalue

Prob message length pkts

(2)

A DT generating WWW browsing traffic (i.e., aWWWbrowsing DT) producespacket callsseparated by areadingtime during a browsing session [11], [12]. A geometricallydistributed number of datagrams ( messages) with mean

is generated per packet call and the datagram interarrivaltime is exponentially distributed with mean rate . Thereading time is exponentially distributed with mean rate.The DT activity factor is

and the mean datagram arrivalrate is msgs/s. We will use [12]:

msg/packetcall, s and msg/s,where1 . The datagram length has thesame truncated and discretized Pareto distribution shown in[11], [12], where bits/msg.

C. Stability Considerations on the Terminal Buffer

We consider here the DT buffer stability (VT buffers have nostability problem, since VTs drop the packets that experience an

1The burstiness degree is the peak-to-mean traffic ratio. A WWW browsingDT (a VT) has a burstinessB = 1= (B = 1= ). For the values assumedhereB � (25 + 8q)=25; the traffic burstiness of a WWW browsing DTincreases withq.

excessive delay). Referring to a DT with a reservation, the meannumber of packets produced by the DT per frame, , mustbe lower than 1 in order to guarantee buffer stability

pktsframe

(3)

Moreover, we consider the VT influence on the DT buffer sta-bility: the sum of the voice throughput and data throughput

in packets per slot must be lower than one. Assuming the DTbuffer stability, must be equal to the total mean input datatraffic: pkts/slot. Therefore, we have

pktsslot

(4)

Conditions (3) and (4) must be jointly used to characterizethe DT buffer stability. Hence, we obtain the following upperbound for : pkts/slot. Thedatagoodput, , [13] is

(5)

The greater (under the constraint for VTs), thehigher the PRMA-HS efficiency.

III. PROTOCOLDESCRIPTION ANDSYSTEM MODELING

We assume that RTD is equal to its maximum value,RTD , for a given LEO satellite constellation (conservativecase). Moreover, the satellite antenna is electronically steeredto point to a given area on the earth for all the satellite visibilitytime (we neglect UT cell changes) [3]. The satellite acknowl-edges the packet used for the reservation as soon as it correctlydecodes its header. We assume RTD , with

and , the packet header transmission time, equal to: a UT receives the outcome of its transmission attempt

made on a slot before the same slot in the next frame. SinceRTD , we have RTD . We consider integer

values of that divide (i.e., RTD contains slots).PRMA-HS allows that a UT may perform new access at-

tempts also while it waits for receiving the outcome of a pre-vious attempt. We assume that the satellite discards any suc-cessful reservation attempt after the first one. Note that thevoice permission probability is greater than the data permis-sion probability in order to prioritize VTs with respect toDTs. We have also assumed anexhaustive service discipline:a UT notifies the satellite of its reservation release by settinganend of reservation flagin the header of the last packet in itsbuffer.

The PRMA-HS protocol can be described by means of VTand DT behaviors, modeled according to the discrete-timeMarkov chains in Figs. 1 and 2 (symbols , , andwill be defined later in this Section), where state transitionsoccur at the end of each slot. Let us focus on the VT statediagram in Fig. 1. As soon as a VT in a silent pause (SIL)generates the first packet of a new talkspurt, it enters thecontending state (CON) and transmits that packet on the firstidle slot according to the permission probability. If the VTattempt has been unsuccessful, the VT remains in the CONstate and can attempt again on successive idle slots; otherwise,the VT leaves the state and goes into a block of hindering

158 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 1, NO. 1, JANUARY 2002

Fig. 1. VT state diagram.

states from HIN to HIN that model thedelay of slots to receive the positive acknowledgmentfrom the satellite. During the time spent in the hindering states,the VT may still try to transmit on available slots, but itsattempts are useless. In the HIN state the VTreceives the positive acknowledgment from the satellite; thus,the VT enters the block from RES to RESthat models the time of slots that is spentwaiting for transmitting on the reserved slot (when the VTreaches RES ). If this is the last packet of the talkspurt, theVT comes back to SIL, otherwise the VT goes to RES .

Since a DT can also receive messages while it is transmittinga given message, a two-dimensional Markov chain is requiredto model the DT behavior (Fig. 2). This chain has an infinitenumber of states; each column of states is for a given numberof messages in the DT buffer. A single state in the VT diagramcorresponds to a row of states in the DT diagram (except forIDLE and SIL states). State variables are defined in Table I; insome cases aggregated variables are considered.

In Fig. 1, is the probability that a VT finds an unreservedslot and obtains the permission to transmit. An analogous defi-nition is valid for in Fig. 2. We have

(6)

(7)

where is the probabilitythat a slot is not reserved.

A VT will obtain the reservation of a slot if no other UTs inCON or HIN states will attempt to transmit on the same slot.Hence, the probability of a successful transmission attempt fora VT, , is shown in (8) at the bottom of the page. The proba-bility of a successful transmission attempt for a DT,, is shownin (9) at the bottom of the page.

IV. SYSTEM ANALYSIS

The standard methods for discrete-time Markov chains [14]cannot be used here, since the PRMA-HS state vector (i.e., the

ifif

(8)

ifif

(9)

BENELLI et al.: PERFORMANCE ANALYSIS OF A PRMA PROTOCOL 159

Fig. 2. DT state diagram.

number of UTs in each state of the diagrams in Figs. 1 and 2) hasinfinite entries. Hence, we have adopted theequilibrium pointanalysis(EPA) [15] to study the system at an equilibrium point,where the expected rate at which UTs leave a state is equal to

the expected rate at which UTs enter the same state [7]. Theequilibrium values (small letters) are:

• , equilibrium number of VTs, DTs respectively inSIL and IDLE state;

160 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 1, NO. 1, JANUARY 2002

TABLE IDEFINITION OF THE STATE VARIABLES

• , equilibrium number of VTs in the CON state,equilibrium number of DTs totally present in CONstates for : , whereis the equilibrium number of DTs in CON ;

• , equilibrium number of VTs in theHIN state, equilibrium number of DTs in the HINstate, where and .We define: and

, where;

• , equilibrium number of VTs in theRES state, equilibrium number of DTs in theRES state, where and

. We define:

and , where;

• , equilibrium number of VTs in the RESstate, equilibrium number of DTs in the RES state,where and . We define:

and , where;

• denotes the total number of UTs that know to have areservation and the total number of UTs in hinderingstates: and

.The previous sums that define, , and are

convergent, since the total number of DTs in the system is finite.The equilibrium values are real nonnegative numbers that can bederived by equating the inflow and the outflow for each possiblestate for VTs and DTs, as shown below.

Voice Subsystem:

Equilibrium at the SIL state (10)

Equilibrium at the CON state (11)

Equilibrium at the HIN states

for (12)

Equilibrium at the HIN state (13)

Equilibrium at the RES states

for (14)

Equilibrium at the RES state (15)

Equilibrium at the RES(0) state (16)

Equilibrium at the RES states

for (17)

Equilibrium at the RES state (18)

where2 [see (19) and (20) at the bottom of the page]. Using(11)–(18), we can obtain (10) and, hence, this condition is re-

2Formulas (19) and (20) are the expressions that at equilibrium correspond toA andU respectively given in (6) and (8).

(19)

if

ifif

(20)

BENELLI et al.: PERFORMANCE ANALYSIS OF A PRMA PROTOCOL 161

dundant. Moreover, the sum of the number of VTs in all thestates must be equal to ; hence, from (12)–(17), we have

(21)

Data Subsystem:The flow equilibrium conditions for thestates in Fig. 2 are summed for the states on the same row (e.g.,CON states, for ). We obtain the following con-ditions:

Equilibrium at the IDLE state (22)

Sum of the equilibria at all CON states

(23)

Sum of the equilibria at all HIN states

for (24)

Sum of the equilibria at all HIN states

(25)

Sum of the equilibria at all RES states

for (26)

Sum of the equilibria at all RES states

(27)

Sum of the equilibria at all RES states

(28)

Sum of the equilibria at all RES states

for (29)

Sum of the equilibria at all RES states

(30)

where,3 similarly to (19) and (20), we have considered (31) and(32) at the bottom of the page.

If we substitute the expressions in (24), (26)–(29) into (23),(25), and (30), we obtain three equations; through algebraic ma-nipulations, these three equations give (22) that, therefore, isredundant. Hence, we have three equations with five unknowndata subsystem variables:, , , , . We add twoconditions. We impose that the number of DTs in all the statesis . From (24)–(29), we have

(33)

Assuming that (3) and (4) are fulfilled, we impose the DT bufferstability: pkts/slot. But ,i.e., the total ongoing flux to RES states from (24)–(29).We have

pktsslot

(34)

Through some algebraic manipulations, (11)–(21) for VTsand (23)–(34) for DTs can be simplified in the following EPAsystem where , , , are unknown terms:

(35)

(36)

(37)

(38)

Since and have transcendent expressions, (35)–(38) havebeen solved with the recursive Gauss–Newton method [16].Once (35)–(38) is solved, is obtained from (23)–(30)as . The EPA solution is acceptable only ifit gives nonnegative equilibrium variable values that fulfillconditions (3) and (4), where is obtained from EPA as thetotal ongoing flux to RES : .

A graphical approach can be also considered for the EPAsystem: for a given couple , we numer-ically solve (36) and (38) to obtain4 and

3Due to the peculiarities of the transitions from RES(j; 0) states in the DTdiagram, the ongoing flux to all RES(j;N � 1) states is equal to the ongoingflux to all RES(j;0) states,r (0), minus the flux from RES(1; 0) to IDLE, (1 � � )r (1;0).

4Onceccc andccc are fixed, we have verified by a graphical approach that thesubsystem (36), (38) admits a single solution.

(31)

if

ifif

(32)

162 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 1, NO. 1, JANUARY 2002

Fig. 3. Graphic EPA solutions forp = 0:6, p = 0:2, T = 15 ms,n = 1,L = 2400 bits/msg and� = 5 msgs/s;solid linesareM curves anddashed linesareM curves.

that are substituted in the right-side terms in(35) and (37) that become functions denoted as and

, respectively. The plane at height intersects thesurface and the plane at height intersects thesurface . The projections of these intersections onthe plane give two curves ( curveand curve)whose intersections identify the EPA solutions. Fig. 3 showsan example of this graphic method for Poisson DTs: thecurve has a monotonic increasing behavior, while thecurvehas an oscillating behavior. For and/or sufficiently low,these curves have only one intersection; if and/or aresufficiently high, there are three intersections (correspondingly,UTs experience time-varyingquality of service(QoS) conditions[7]). We will we only consider cases with one EPA solution(equilibrium values equal the mean state variable values [7]).

V. PERFORMANCEEVALUATION

In order to obtain , we refer to a VT starting a newtalkspurt (i.e., it leaves the SIL state) when there areandUTs in the CON state, and UTs in HIN states, andand UTs in RES and RES states. Accordingly, we compute

conditioned on the aggregated state, whose joint probability distribution

is derived in the Appendix. Since we require, we can reasonably neglect the possibility that a

VT drops an entire talkspurt [9]. Let us consider first the caseswith (not all the slots are reserved).

The conditioned probability that a VT successfully transmits apacket on a slot, , is

(39)

where is shown in (6) is given by (8) and where weconsider VTs in the CON state.

The random number of slots spent by a VT in the CON state toobtain a reservation conditioned on ,

, has the following geo-metric distribution:

for (40)

Hence, is obtained as fol-lows [7]:

for (41)

where and . denotes theceiling function.When , we have from (39) that

is equal to 0 and the distributionof in (40) degenerates. Thisis due to the fact that (39) does not consider that a reserved slotmay be released during the access phase. We neglect this aspectfor a conservative evaluation. Hence, when all the slotsare reserved, analogously to [17], we have

for (42)

We remove the conditioning on by using the distribu-tion . Since, according to our as-sumptions, there is at least one VT in the CON state, we con-sider the conditioned distribution

Prob

On the basis of the Appendix, we have Prob. Hence, results in (43) at the bottom of the

page, where

(43)

BENELLI et al.: PERFORMANCE ANALYSIS OF A PRMA PROTOCOL 163

is the maximum number of slotsthat can be reserved by VTs: cannot exceed thenumber of slots per frame and the number of VTs thatcan have a reservation5 i.e., ;

is the maximum number ofslots that can be reserved by DTs: can not exceedthe number of DTs in the system and the number ofslots per frame not reserved by VTs;

isthe maximum number of VTs in HIN states: cannot exceed the maximum possible number of UTs inhindering states,6 the number of unreserved slots andthe number of VTs without a reservation minus one,7

i.e., ;is

the maximum number of DTs in HIN states: cannot exceed the maximum possible number of UTs inhindering states,8 the number of unreserved slots andthe number of DTs without a reservation;

is the maximum number of VTsin the CON state: is equal to the number of VTsin the system minus those already having a reservationminus one;9

is the maximum number of DTs inCON states: is equal to the number of DTs in thesystem minus those already having a reservation.

We consider here Poisson DTs to analyze . Hence, themanagement of messages in each DT buffer can be modeledas an queuing system ( : Poisson arrival process

: general service time distribution/1 server since a DT cantransmit a message at once with one slot reservation) withdifferent message service times, whether a message arrives atan empty DT buffer or not (in this case this message does notexperience an access delay). We embed the queuing system atthe message transmission completion instants. Let denotethe service time inslotsfor a message arrived at the DT bufferwhen it is empty (not empty). From the theory and theLittle’s formula [14], we have

slots (44)

Let denote the random variable of the message length inpackets; . Letdenote the time spent by a DT in CON states in order to make asuccessful attempt, assuming that when this DT leaves the IDLEstate it finds and UTs in CON states, and UTs in

5This value takes into account that at least one VT has not a reservation tostart a new contending procedure.

6At most, we can have a UT waiting for an acknowledgment for each delayfrom 1 toN=n slots.

7This value takes into account that at least one VT has not a reservation tostart a new contending procedure.

8At most, we can have a UT waiting for an acknowledgment for each delayfrom 1 toN=n slots.

9This value takes into account that at least one VT has not a reservation tostart a new contending procedure.

HIN states and and UTs that know to have a reservation.Hence, we express and as follows:

slots (45)

slots (46)

The distribution of is defined by (2), whereas the distribu-tion of is formally given by(40), where subscript is replaced by . The mean and the meansquare value of both andare

(47)

Hence, we obtain and from (45) by usingand given in (47). Whereas, in order to have

and from (46), we must remove the conditioning onthe state in both and

. On the basis of (47),these expressions are singular when (i.e., all theslots are reserved, ). Correspond-ingly, the distribution ofdegenerates. This is due to the fact that we have neglected therelease of slots during the access phase of a UT. Therefore,

accounts for both the time for the first release of one reservation,and

the time to obtain a reservation starting from a situation withreserved slots,

. Hence, we have

(48)

Sinceand

are independent variables, we can easily obtain themean and the mean square value of

. Inwe assume

that is reduced by one with respect to, so

that ; hence, the distribution ofis given

164 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 1, NO. 1, JANUARY 2002

by (40) with subscript instead of . Moreover, we considerthatis geometrically distributed

for (49)

where the probability to release the reservation of a slot,, is obtained as follows: a VT

releases the reservation with probability , whereas a DT re-leases the reservation with the probability that it has transmittedthe last packet of the last message in its buffer and no othermessage arrival occurs on this slot, .These probabilities are respectively weighted by the probabilitythat the slot is reserved by a VT, and by a DT,

. We have

(50)

Finally, we remove the conditioning inand

by using the joint state distribution and the normaliza-tion factor Prob ,since at least one DT must be in the contending state (seethe Appendix). We have (51) at the bottom of the page.

, ,,,

, .

VI. RESULTS

Each simulation has been very long (20010 slots) and re-peated ten times to obtain reliable results [18]. We focus here ona communication system with kbs/s, kb/s,and bits where the EPA system admits only one solu-tion and where (3) and (4) are fulfilled (DT buffer stability).

A. Selection of System Parameter Values

Simulation results have shown that has unacceptablyhigh values when is close to 0 or 1 (for low values, VTs

Fig. 4. Efficiency comparison between PRMA-HS, PRMA and TDMA forM = 10 DTs/carrier,L = 22560 bits/msg,� = 0:3 pkts/slot,n = 1

and the selected values forp , p .

do not quickly access slots; while, for very highvalues, VTsexperience frequent collisions). In general, is a goodchoice. Moreover, slightly depends on : only whenis close to 1, increases owing to frequent collisions be-tween DT and VT attempts. When and are close to 1,

exhibits a peak due to frequent collisions; moreover,increases when , since accesses are delayed. In conclu-sion, we have set and to prioritize VTs asregards DTs.

Let denote the maximum number of VTs that canbe served by a PRMA-HS carrier with . Due tothe presence of DTs, the quantityrepresents the maximum number of slots that can be used byVTs in an ideal TDMA carrier (i.e., without packet overhead).We define theVT multiplexing gain, , expressed inconversa-tions/voice channelas the ratio between and

. If conversations/voice channel,PRMA-HS achieves a more efficient VT management than theideal TDMA scheme. Fig. 4 shows behaviors as a functionof (i.e., RTD , since ) for a given configuration byusing the previously selected values ofand . We note that:1) PRMA-HS is more efficient than TDMA on a wide rangeof values and 2) PRMA-HS outperforms PRMA especially

(51)

BENELLI et al.: PERFORMANCE ANALYSIS OF A PRMA PROTOCOL 165

Fig. 5. Comparison between simulation results and analytical predictionsfor P with M = 21 VTs/carrier,M = 10 DTs/carrier,L =

2400 bits/msg,n = 3 and the selected values forp , p andT .

Fig. 6. Comparison between simulation results and analytical predictionsfor T with M = 21 VTs/carrier,M = 10 DTs/carrier,L =

2400 bits/msg,n = 3 and the selected values forp , p andT .

from medium to high RTD values. A similar behavior asa function of can be obtained with WWW browsing DTs.Therefore, of PRMA-HS is high for ms; wechoose ms (correspondingly slots/frame),since this value allows the lowest . The following resultshave been therefore obtained by using , and

ms.

B. PRMA-HS Performance Evaluation

Figs. 5 and 6 compare simulation and analytical re-sults as a function of with bits/msg,

VTs/carrier, Poisson DTs/carrier and; in abscissa varies due to the message arrival rate

increase from 1.4 to 12.6 msgs/s. Fig. 5 shows thatincreases with and that the theory gives an upper boundsufficiently close to simulation results (especially whenranges from to ). The maximum value with

is about equal to 0.9, so highlighting an efficientresource management. Fig. 6 also shows a good agreementbetween simulation and analytical results for .

Figs. 7 and 8 show and behaviors forVTs/carrier, Poisson DTs/carrier and with

and 0.4 pkts/slot as a function of . From Fig. 7,we have that the theory allows a conservative estimation,close to simulation results. Moreover, Fig. 8 highlights that theproposed analytical approach for yields an accurate esti-mation.

Fig. 7. Comparison of theP theory with simulation results forM =

21 VTs/carrier,M = 10 DTs/carrier,� = 0:3 and 0.4 pkts/slot,p = 0:6,p = 0:2, T = 15 ms,n = 1, as a function of the message lengthL .

Fig. 8. Comparison of theT theory with simulation results forM =

21 VTs/carrier,M = 10 DTs/carrier,� = 0:3 and 0.4 pkts/slot,p = 0:6,p = 0:2, T = 15 ms,n = 1, as a function of the message lengthL .

Figs. 9 and 10 present and behaviors ofPRMA-HS as functions of , for different RTD valueswith VTs/carrier, Poisson DTs/carrier,and bits/msg; we have considered three cases:RTD ms (i.e., , typical LEO altitude),RTD ms (i.e., , very low LEO altitude), andRTD (i.e., , terrestrial cellular system wherea UT knows the outcome of a transmission attempt withina slot time). In these figures, we have also shown PRMAresults. As expected, PRMA-HS is quite insensitive to differentRTD values and significantly outperforms PRMA fromlow-to-medium data traffic loads in terms of both and

.Let us focus on the impact of the DT traffic type on both

PRMA and PRMA-HS. We assume VTs/carrier andDTs/carrier; we consider a first case with WWW

browsing DTs and another case with Poisson DTs. ForPoisson DTs, the mean message length and the mean messagearrival rate have been considered equal to the correspondingones shown in Section II for WWW browsing DTs. Figs. 11and 12 show and results as a function of parameter

(for WWW browsing DTs) or the equivalent value DT.Fig. 11 highlights that PRMA-HS significantly outperformsPRMA in both the DT traffic cases. Moreover, the value

166 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 1, NO. 1, JANUARY 2002

Fig. 9. P behavior for PRMA and PRMA-HS withp = 0:6, p = 0:2,T = 15 ms,M = 21 VTs/carrier,M = 10 DTs/carrier,L =

2400 bits/msg and for RTD = T =n.

Fig. 10. T behavior for PRMA and PRMA-HS withp = 0:6, p =

0:2, T = 15 ms,M = 21 VTs/carrier,M = 10 DTs/carrier,L =

2400 bits/msg and for RTD = T =n.

Fig. 11. P behaviors for both PRMA and PRMA-HS as a function ofqfor M = 21 VTs/carrier,M = 12 DTs/carrier,p = 0:6, p = 0:2,T = 15ms andn = 1: solid linesare for the cases with Poisson DTs;dashedlinesare for the cases with WWW browsing DTs.

in the presence of WWW browsing DTs is slightly higher thanwith Poisson DTs, since the greater the data traffic burstinessthe higher the congestion of the contending state. As for ,the scale adopted in Fig. 12 does not allow to highlight theadvantages (on the order of tens of slots) of PRMA-HS with

Fig. 12. T behaviors for both PRMA and PRMA-HS as a function ofqfor M = 21 VTs/carrier,M = 12 DTs/carrier,p = 0:6, p = 0:2,T = 15ms andn = 1: solid linesare for the cases with Poisson DTs;dashedlinesare for the cases with WWW browsing DTs.

respect to PRMA (the main contribution to is due to thedatagram queuing rather than to the access phase). Finally,

significantly increases in the WWW browsing case withrespect to the Poissonian one, due to both the high datagramlength variance and the bursty traffic that causes a suddenqueuing of datagrams.

VII. CONCLUSION

In this paper, we have proposed the PRMA-HS protocol tosupport voice and data traffics in LEO-MSSs. Suitable trafficmodels have been considered for both voice and data sources.The PRMA-HS performance has been evaluated in terms ofpacket dropping probability for VTs, and mean messagetransmission delay for DTs, . Analytical predictions forboth and have resulted in agreement with simu-lation results. In conclusion, it has been highlighted here thatPRMA-HS efficiently manages voice and data traffics in LEO-MSSs and clearly outperforms the classical PRMA protocol.

APPENDIX

DERIVATION OF THE JOINT STATE PROBABILITY DISTRIBUTION

Using three times the Bayes rule, the joint state probabilitydistribution is

(A.1)

where is the distribution of and where ,are condi-

tioned distributions.Each slot has the same probability to be reserved and slots are

independently reserved by VTs with probability . Hence,the probability of slots reserved by VTs is binomial

and (A.2)

BENELLI et al.: PERFORMANCE ANALYSIS OF A PRMA PROTOCOL 167

Since we refer to cases with a single EPA solution, we obtainby equating the mean value of to the corresponding

equilibrium value. From (11)–(18), we have

(A.3)

We define as the probability that a slot is reserved by aDT conditioned on slots already reserved by VTs. We con-sider the following binomial distribution for :

and (A.4)

Probability is obtained by equating the mean of toits equilibrium value

(A.5)

In order to derive we use the Bayes ruleas follows:

(A.6)Both and are assumed

binomial, since each unreserved slot has the same probabilityto be successfully occupied by a UT that enters the hinderingstates. Hence, we have

and

(A.7)

and

(A.8)

where is the conditioned probability that a VT(DT) is in a HIN state (in a row of HIN ( ) states). Equatingexpectations of and to the corresponding equilibriumvalues, we have (A9) at the bottom of the page. We made twoassumptions for : 1) andare statistically independent and 2) the number of VTs (or DTs)in the CON state is independent of the number of DTs (or VTs)in HIN, RES or RES states. These assumptions are reasonablein a noncongested system, i.e., when and (as itoccurs if ) so that there are few collisions betweenDT and VT attempts. We have

(A.10)

where and can be modeled astruncated geometric distributions [9]. See (A11) and (A12) atthe bottom of the page. and respectively denote theprobability of no VT and no DT in the contending state. Proba-bilities and are derived by equating the expected valuesof and to their equilibrium values. We have numeri-cally verified that a good approximation for the solution of theseequations is

and

(A.13)

ACKNOWLEDGMENT

The authors wish to thank Dr. Ing. F. Bossoli for providinguseful comments and discussions.

and

(A.9)

if

ifotherwise

(A.11)

if

ifotherwise

(A.12)

168 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 1, NO. 1, JANUARY 2002

REFERENCES

[1] “Special issue on IMT-2000,”IEEE Pers. Commun. Mag., vol. 4, Aug.1997.

[2] I. Mertzanis, G. Sfikas, R. Tafazolli, and B. Evans, “Protocol architec-tures for satellite ATM broadband networks,”IEEE Commun. Mag., vol.37, pp. 46–54, Mar. 1999.

[3] J. Restrepo and G. Maral, “Constellation sizing for non-GEO ‘Earth-Fixed Cell’ satellite systems,” inProc. AIAA 16th Int. CommunicationsSatellite Systems Conf. and Exhibit, Washington, DC, Feb. 25–29, 1996,pp. 768–778.

[4] V. Leung, H. Alnuweiri, and P. Nasiopoulos. Interworking broad-band satellite networks with terrestrial networks subsystems.Univ. British Columbia. [Online]. Available: http://www.ece.con-cordia.ca/~hamid/majorp4.html

[5] D. P. Connors, B. Ryu, and S. Dao, “Modeling and simulation of broad-band satellite networks Part I: Medium access control for QoS provi-sion,” IEEE Commun. Mag., vol. 37, pp. 72–79, Mar. 1999.

[6] D. J. Goodman, R. A. Valenzuela, K. T. Gayliard, and B. Ramanurthi,“Packet reservation multiple access for local wireless communications,”IEEE Trans. Commun., vol. 37, pp. 885–890, Aug. 1989.

[7] S. Nanda, D. J. Goodman, and U. Timor, “Performance of PRMA: APacket voice protocol for cellular systems,”IEEE Trans. Veh. Technol.,vol. 40, pp. 584–598, Aug. 1991.

[8] E. Del Re, R. Fantacci, G. Giambene, and S. Walter, “Performance eval-uation of an improved PRMA protocol for low earth orbit mobile com-munication systems,”Int. J. Satell. Commun., no. 15, pp. 281–291, 1997.

[9] , “Performance analysis of an improved PRMA protocol for lowearth orbit mobile satellite systems,”IEEE Trans. Veh. Technol., vol. 48,pp. 985–1001, May 1999.

[10] Y. Corovesis and D. Venieri, “New user and service requirements,”, IN-SURED Project (AC229).

[11] “Selection procedures for the choice of radio transmission technologiesof the UMTS (UMTS 30.03 Version 3.1.0),” European Telecommunica-tions Standards Institute, Sophia-Antipolis, France, 1997.

[12] A. E. Brand and A. H. Aghvami, “Multidimensional PRMA with priori-tized Bayesian broadcast—A MAC strategy for multiservice traffic overUMTs,” IEEE Trans. Veh. Technol., vol. 47, pp. 1148–1161, Nov. 1998.

[13] S. Rosenberg, M. Aissaoui, K. Galway, and N. Giroux, “Functionalityat the edge: Designing scalable multiservice ATM networks,”IEEECommun. Mag., vol. 36, pp. 88–99, May 1998.

[14] L. Kleinrock, Queuing Systems. New York: Wiley, 1976.[15] A. Fukuda and S. Tasaka, “The equilibrium point analysis—A uni-

fied analytic tool for packet broadcast networks,” inProc. IEEEGLOBECOM’83, San Diego, CA, Nov. 1983, pp. 33.4.1–33.4.8.

[16] Matlab—Reference Guide, Math Works, Natick , MA, 1992.[17] H. Qi and R. Wyrwas, “Markov analysis for PRMA performance study,”

in Proc. IEEE Vehicular Technology Conf., Stockholm, Sweden, June7–10, 1994, pp. 1184–1188.

[18] P. J. Smith, M. Shafi, and H. Gao, “Quick simulation: A review of im-portance sampling technique in communication systems,”IEEE J. SelectAreas Commun., vol. 15, pp. 597–612, May 1997.

Giuliano Benelli received the degree in physics fromthe University of Florence, Florence, Italy, in 1973.

He is Full Professor at the Engineering Facultyof the University of Siena, Siena, Italy, where heteaches Electrical Communication Networks. In1975, he joined the Electrical Department of theUniversity of Florence, first with a ResearcherFellowship and from 1981 to 1987 as a Researcher.From 1987 to 1990, he was an Associate Professorat the Engineering Department of the University ofFlorence, where he taught Telecommunication Sys-

tems. From 1990 to 1993, he was a Full Professor at the Electrical Departmentof the University of Pavia, Italy, where he taught Electrical Communications.His main interests are image processing and transmission, channel coding,modulation, and digital networks. In the last years, he addressed his principalintersts to networks, multimedia applications and telematic services.

Romano Fantacci (S’82–M’87–SM’91) was bornin Pistoia, Italy. He received the Dr. Ing. degreein electronics engineering from the University ofFlorence, Florence, Italy, in 1982, and the Ph.D.degree in telecommunication engineering in 1987.

In 1982, he joined the Electronics and Telecommu-nications Department of the University of Florence,first as researcher, then as Associate Professor andcurrently as Full Professor of TelecommunicationNetworks. During the first stage of his researchactivity, he worked on satellite communication

systems. In particular, he has been involved in several European Space Agency(ESA) and INTELSAT advanced research projects. His present researchintersts involve digital communications, computer communications, queueingtheory, fast packet switching, and mobile communication networks. He is theauthor of several publications, some of which have been published in the mostacknowledged journals in communication science. He has been also involvedin several European and nationwide research projects.

Giovanni Giambene received the degree inelectronics in 1993 and the Ph.D. degree in telecom-munications and informatics in 1997, both from theUniversity of Florence, Florence, Italy.

From 1994 to 1997, he was the Electronic Engi-neering Department of the University of Florence,where he supplied the task of Technical ExternalSecretary of the European Community ProjectCOST 227. He also contributed to the “ResourceManagement” Activity of the Working group 3000within the RACE II Project called (SAINT, RACE

II). From 1997 to 1998 he was with OTE of the Marconi group, where he wasinvolved in a GSM development program. In the same period, he contributed tothe research activities of the COST 252 project by studying new medium accesscontrol protocols for voice and data transmissions in low earth orbit mobilesatellite systems. Since 1999, he has been with the Information EngineeringDepartment of the University of Siena, Siena, Italy. His research intersts dealwith the performance analysis of radio resource management schemes andmedium access control protocols for future terrestrial and satellite mobilecommunication systems.

Carlo Ortolani was born in Verona, Italy, in 1970.He received the Dr. Ing. degree in telecommunica-tions from the University of Florence, Florence, Italy,in 1998.

In that period, he was involved with the Electronicsand Telecommunications Department of the Univer-sity of Florence on a research activity dealing withthe definition of MAC protocols for voice and datatransmission in mobile satellite systems. Later on, hewas with CSELT S.p.A., Turin, Italy, for the realiza-tion of the GSM project supported by Telecom Italia

Mobile S.p.A. At present, he is a systems integrator with Telecom Italia S.p.A.