A Burst-Level Adaptive Input-Rate Flow Control Scheme for ATM Networks Izhak Rubiii Electrical Eiigiiieeriiig D e p r t men t ‘IJniversity of Califorilia a.t Los Angeles Los Angeles, CA 90024

U

Abstract W e propose a iieru ziipiti rutc p o w conirol scheme wherezii the credat aitcreinent role as updated periodically as ihe loadaiig slatus uaries. Based upoi, the observed s i a i u s of each siriiioii s’ burst-level ncizoiiy, ihe network access it ode daslidmtes feedback coiiirol sagnalzng messages l o the stalions. T h e s e sagnalziig messages a//o?ii ihe siaiaons i o a d a p i ihezr credal ai)creiiieiti rates a n accordaiice wath s y s t e m bursi-loadaiig condations W e preseiil queueing models i o s i u d y the sysieni performance at Ihe access poai,is of sucli 11 sysiein For this purpose, w e select a sub-iietwork topology whzch ziivolves a network swatch (such as a f a s t packet swatch zn high-speed metropolatan o r wade area networks) aiid a n~iiiiberof regiilnled source sioiaons whzch dniie the network swatch. T o avoad packel retran siiiasszoiis due i o cell losses at the access sruztclt, each iiser siatioii (or CPN) zinplements locally a replica of the input regnlation schenie. The oulpiil I r a f i c streains froin the source stalzoiis. as r e g d o l e d by ihc local ziipiii rale coiitrol niechanzsm (and adayled b y Ihe staliis messages), load a packet swatch whzch i s modeled as a inultaples e r v e r queueing s y s t e m . Performance curves are presented t o allusirate the slaiislacal qiteue-szze behariaor and message delays at both the ,source slations and the ii e 1 work swzl ch.

1

Iiitroductioii

Rate-based access control schemes have been shown to provide an effective inechanisin for the regula.tion of traffic streams accessing a high-speed coinmun ic a.tion network . Tra.di tion a 1 w i lido w based endto-end flow cont,rol schemes alone are insufficient. as t,he speed of transmission increases, due t.o the Ion associated end-to-end delay la.t.encies incurred [I& BELLCORE’s Switched Multi-mega.bit Da.ta. Service (SMDS)[16], IBM’s Packetized .4utoma.t.icRouting Integrated System (PARIS)[S], and inult,it.udeof FrameRelay switching systems are examples of high-speed networks which implement input ra.te flow control mechanisms. For a network supporting SMDS, an input rate control mechanism (identified as a Credit Manager Algorit.hm) is enacted t,o reguhte tra,ffic between Customer Premises Equipment ( W E ) and a

I<. David Liri Science & Technology S MiEST Advanced Technologies Boulder. CO 80303

MAN Switching Syst,em (MSS). ATM (Asynchronous Transfer Mode) networks which provide support for l3ISDN services also use input rate flow control schemes. In this paper, we assume that each user-station implemeiits a replica. of the input rate control mechanism. At the network switch, received user segmeiit.s which violate the traffic contract inay be blocked or treated as lower priorit,y messages by t.he network policing unit. Consequently, it is highly advantageous for user-st,a.tions t*oregulat,e their own traffic so t,ha.t packets or cells) tra.nsmit,ted into the network ha.ve a good c(I miice of being accept,ed by t,he network. In this inanner, packet, (or cell) retransmissions clue to cell losses induced by viola.tions of the rat.e regula.tion scheme are significant.ly reduced. This is of critica.1 importa.nce for the provision of acceptable gra.de of service (as well as xceptable sequencing and delay features) for many a.pplica.tions. Hence, throughout this pa.per, we assume t1ia.t. each user sta,tion employs a device which iniplement,s locally t,he underlying input. ra,t,econt,rol scheme (as it, should apply to i t s station, in a.ccorda.nce with i t.s negotiated a.ccess pa.ra.met,ers) a.nd delays/bufTers its inessages when the traffic contract. doesn’t allow a.dditional traffic from t,he user stat.ion t,o access t.he net.work. See also [I, 8, 10, 131. It has been shown that, the system’s performance ca.n be improved by the use of a. mechanism which a.llocat,es access-rate pa.raineters (credits) to user s6at.ions dynamicaHy, rather than on a. fixed basis. See [a, 2, 7 , 121. Traffic streams which correspond to many B-ISDN applications t,end to be highly bursty. The statist,ical fea.t.uresof such streams a,re that their activit,ies, while in session, a.lternate between “burst” periods (“on” periods) a i d “idle” periods (“off” periods). Such periods can be of rela.tively long durations. U i i der a static input rate control scheme such as Credit. Manager Algorithm (or Leaky Bucket scheme), the a.ccess rate of each user stat,ion is assigned i n a static fashion. The statistically bursty features of the traffic streams are not utilized. I n this paper, we present a new Feedback Scheme that utilizes this burst level information and applies it as feedback messages directed to the input rate cow trol iiiecha.nism of each sta.tion to determine the station’s appropriate credit increment rate. The access rate of ea.ch source station is thus dynainically updated to accommodate the statistical features of the

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traffic streams. Since many applica.t.ions induce highly bursty streams which, once active, tend to sta.y active for a long duration, a significant reduction in the feedback signaling rate is achieved. We denionstra.te i n this paper the performa.nce fea,t,ures and a.dvant.ages exhibited by such an a.da.pt.ive input.-ra.te regula.tion method. This paper is orga.nizec1 as follows. In t,he next section, we describe tlie operation of this new Feedback Scheme. In section 3, we present queueing models and an analytical a.pproa.ch to study the effect of this a.daptive input rat*econtrol scheme on the queue sizes and messages delays a t t,he source sta.tions a.nd a.t. the network switch. In section 4, numerical examples and performance curves a.re provided to illustrate the methodology developed in this pa.per. Conclusions are drawn in section 5.

2

The Burst Level Feedback Scheme

Typical B-ISDN tra.ffic streams offered to ATM networks are bursty or highly bursty; exa.mples include streams that, correspond to applica.tions involving video, imaging, still picture, a.nd packet voice [3, 4, 141. Such traffic streams are often stochastically characterized‘ as genera.ted by a. Markov Modulated source which is governed by two modes: Idle mode and Burst mode. T h e duration of t,he each mode is typically very long as compa.red with the t~ransmission time of a single cell (a slot). Assuming a t.ra.nsmission rate of the access link to be equal to 150 Mbps, and noting that a single AThl cell contains about 500 bit.s, the transmission time of a cell is roughly 3.3 p sec. Using the modeling exa.mples present,ed in [4], t,he a.verage “on” period of a burst generated by packet, voice is 352 ins, which transla.tes into about 100,000 slots; the average burst’s “off period is 650 ins, equa.1 t.o about 200,000 slots. Tlie average burst. level L‘o~i’’ and “off durations of still pict,ures are, for example, 500 ins and 11,000 nis, respectively. These correspond t o 150,000 slots and 3,333,000 slots, respectively. Under the Credit Manager Algorithm (CMA), as presented in [l, 10, 131, tlie bandwidth allocated to a subscriber-to-network or user-to-network interface (SNI or UNI) link (credit, increment d e ) is st.a.t.ic, as illustrated in Figure 1. Tlie opera.t,ion of a station regulated by a CMA is described by a model which consists of a cell queue a.nd a credit. (t*oken)queue. A fixed amount of credit is generated periodically. Arriving messages are decomposed into fixed-length cells. A single credit is required (a.nd exhaiist,ed) for t.he t.ra.nsmission of a single cell. Since a replica of the CMA (implemented at the network’s access switch) is also implemented by the user’s station a t tlie SNI/UNI, cells are queued a t the user’s buffer when no credit is available for their transmission. Tlie cell queue is assumed to have an infinite buffer size. Tlie credit queue has a maximum buffer size equal to C,,,,,.. Credit. is generated a t a constant, ratmeunt,il C,,,,:, is reached. T h e unused credit, is stored i n t,he credit queue. W e set the transmission time of a. cell t.0 be equa.1t,o 1 time slot. Let tlie station’s credit generat,ion rate be set, a t

[credits/slot,], so t,ha.t H credit,s are generated a t the start of every Ir’ slot,s, H 5 K . Thus, the average a.ccess ra.t,e across the stfation’s dedicated link to the network is equal to ~[cells/slot].We divide time into consecutive frames, each consisting of a consecutive collection of K slots. Under the Burst Level Feedback Scheme proposed here, tlie credit increment rate of a user station is dynamically updated. A signaling sub-channel is established between tlie network access switch and the user stations. When the credit increment rates for user stai tions require to be changed, the network access switch sends uotification messages to user stations through this sigualing sub-channel. Tlie credit increment rate assigned t o ea.ch user station is determined (at the start of every frame) by the total number of active stations (the number of stations that are in an active statme,and thus identified to be in the “on” mode at. t.he burst. level). .4ssuiiie t,lia.t, blie network switch 60 allocate a total of L credits per frame to these active stations among a total of A4 source stations accessing this switch. If N out of these A4 stations are currently in their modes, tlie Burst Level Feedback Scheme divides and equally distributes these L credits to the N a.ctive stations, while assigning a single credit to each of tlie A4 - N idle stations. Each station sends a burst status signaling message t o the network swit.c.lit,o indica.te a change in the burst mode between tlie “ou” and ‘‘off’’ states. The network switch then sends feedback messages to each station notifying them about tlie underlying credit re-allocation. This informa.tioii is used by each source stcationto incorporate it,s alloca.ted credit. quantum within its operated CMA.

3

Queueing Models

In this section, we present queueing inodels to analyze the system performmce of tlie source stations and the network switch. Our system and queueing model for such a system is presented in Figure 2. Tlie queueing system model consists of two stages: the first. st.a.ge represei1t.s t,lie sourcc s t a h i s and (.lie second stage involves tlie network switch. Each source station is modeled as a queueing system whose service rat.e is controlled by t.he underlying Burst. Level Feedback Control mechanism. Arriving messages, as generated by the applica,tion processes, are decomposed into cells. Cells are st,ored at. the buffer of the user’s stmation when they ca,nnot be tra.nsmitted. These buffers are assumed t o be of unlimited size. T h e regulated traffic streams a t the output of the from source stations load tlie network switch. T h e switch is modeled as an L server queueing system with a limited buffer size. By choosing the parameters of the input rate regulating mechanisms properly, tlie resources of the network can be prot,ect,ed and accept,ahle packet. queueing delays at. the source station a.nd a t the switch are ensured, so tha,t. acceptable end-to-end message delay and blocking performa.nce can be guaranteed.

387

3.1

A Queueing Model for the Source Stations

flow control, as present,ed in tlie following

The following queueing model for t,lie source stations is assumed. Time is segmented into fixed-leiigth slots. Each slot durat,ion is equal to the transmission time of a cell. A frame consists of a coiisecutive group of IC slots. Credits are incremented a t the start of each frame. We assume each station to generate tra.ffic in accordance with a Markov Modulated Process. The latter is stochastically characterized by tlie variables EAm),n 2 l} as delineated below. The following variables are then defined. For 911 = 1,2,. . . , Ad, we have:

{Aim,”),

XAm):System size of station 771. (number of cells queued i n the source station’s buffer ) at the start of frame n; A’, = 0 , I , 2 , . . ..

CAm): Credit available to statmionin at the start of frame n; c!?’= 1 , 2 , . . . , c $ ~ ~ ~ .

E?): Burst, a.ctivit>yindex of station i n at. t.Iie start. of the n-th frame. E!?) = 0, when stat.ion i n is idle during the 71.-th frame. E r ’ = 1, when = station ni is active during the n-tIi frame. {E?), n, 2 1) is a.ssumed t,o be a kiarkov Chain for = 1 , 2 , . . . , A4, with a transition probability function, pi;), i , j E ( 0 , I ) .

Aim,”):Number of a.rriving cells t,o sta.t.ion 772 during the 11.-th frame, as recorded at, the end of frame 11,; w~ienE : ~ )= 1, the possillle values are A?) = 0 , 1 , 2 , .. .; w~ienE?) = 0 , A!,T) = 0. w e assume { A ? ) , n 2 l} to be a sequence of independent random variables. We set P (A::’ = ilE,(F) = 1) = aim),i 2 0, a.nd it,s mean to be A(”) = E,: i . ai < 1, expressing the mean burst-level arrival rate in [celIs/fra~tne]for st,a.tion i n .

Fp):Amount of credit iiicrement a.llocated to sta= tion m a t the start of the n-t,~]frame; F?’ 1,2, . . , K. ‘

DA”:

Number of departing cells (i.e., cells transmitted across the user-to-network a.ccess link) from regulated source station 772 during frame n; oAm=) 0 , 1 , 2 , .. . , Ii.

Cells arriving a t a user station witJiin a. frame a.re considered for transmission across the SNI/UNI link a.t. the start of the next frame. Denote I ( f l a g s ) to be an indicator function such that it equals 1 when all its flags are true and 0 otherwise. Recursive equations are written to describe the operation of the input rate

-4s expressed by Equation ( l ) ,under the Burst Level Feedback Scheme. an idle sta.tion is assigned a credit.

increment. equal to 1 [credit,/fra,me], while all burstlevel a.ctive stations share a total of L credits per frame. In [ill, we present a. model for t.he system-size process of a source station regulated by the static Credit Mana.ger Algorithiii with credil incremented by an fixed amount. h every li’ slots. Ilnder this model, the a.rriva1 process is always in itas“on” mode; i.e., we set. FAT! = h in Equation ( 5 ) ,and I$,’$’;’ = 1 and pi;) = 0 for t,he arrival process. In this paper, we also present a numerical technique for the calcula.tion of the steadystate system-size dist,ribut>ionat a reguhted station. A s noted in the previous section, the burst duration is typically very long compared to the transinission time of a cell. Consequently, we now assume the number of user statlions which siniultaneously reside at the active burst (“on”) mode to not change over a. long period of time. Under this assumption, tlie credit increment rate process is quasi-sta.tionary. The steady-state behavior of tlie system-size process at the user sbation’s buffer ca.n therefore be analyzed using the following approach. To analyze the system performance under the Burst Level Feedback Scheme, we define the steady-state distribution of the system-size process at station ni as:

ny)=

lini P ( x ~ =) x). 71-w

(8)

The probabilit>yt,hat, station m.is i n the “on” mode is clearly given by:

(9)

We assume that pi:) << 1, p!:) << 1, for each m , since tlie underlying bursty stations stay for relatively

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long periods of time in active as well as idle burst. periods. Hence, by using the quasi-stationary modeling assumption, we conclude:

relatively long period of time, setting x ( ~= )o a t steady-state (for a randomly selected slot within tlie idle period) yields a very tight approximation.

3.2 h‘ h=l

C

where

and X!,”)(h) and C?’(h) are variables representing the system size and credit available a t station 171, at the start of the n-th frame when its credit is incremented by a fixed amount /I every frame, and that the arrival traffic is continuously i n the “on” mode with probability 1. FLm)is the probability that station m’s credit is increment,ed by /i every frame when it is active; i.e.

By using E uations (lo)-( 13) and the solution techwe obtain tlie system size dist,ributions nique in a t the buffer of the source stations. We then obtain the mean and the moments of the system size variable and the mean delay of a randomly selected cell by using Little’s Theorem. In writing Equations (10)-(13), we have also assumed that the ( h ) ,CAm)( h ) ,t i 2 I} is joint Markovian process S,(F)

[lll,

{

positive-recurrent (ergodic) for each selected value of h , 1 5 h 5 IC. Thus, station tn is assumed to experience a stable queueing operation under an average access rate of h = 1 [celI/frame]. (It is then also stable for h > 1.) A necessary and sufficient condit,ion for such a condition to hold is given by A(”’) < 1 , m 2 1. Note t1ia.t due t,o t.he long residence time of each station in an active burst, mode, it, is necessary t.o provide the station with the a.bove ment,ioned service rate ( h = 1) to guarantee a.ccepta.ble levels of cell delays at the source buffer under this condition. Clearly, when other stations are not active the active stations are provided with higher access rates ( h > 11, leading to lower system-size and delay levels at. the source buffer. Also note that we have set in Equat,ion (10) that station’s system-size to be equal to 0 (X(”’) = 0) when this station is in an idle (“off”) burst mode. Clearly, following a transition from active t o idle burst modes, the station’s system-size will gradua.lly approach an empty state. However, since the station experiences a stable service operation during an a.ctive burst, mode, and since the subsequent idle burst mode la.sts for a

A Queueing Model for the Network Switch

In this section, we continue to employ the quasist.a.t.ionary assumpt,ion on the credit, increment. rat.(= processes at the source stations and analyze the system-size process a t the network’s switch. In [ll], we present a characterization of the departure process from a source station whose credit is incremented by h every IC slots, when the arrival process to that source station always stays in the active (“on”) burst mode. In this paper, we also present a technique for the calculation of the steady-state distribution of the syst.em-size a.t. the switch’s buffer when it is loaded by A 4 regitlat,ed source st,at>ionswhose depa.rture processes are cliaract,erized in the paper. As observed previously, t.he number of simultaneously active user stations does not fluctuate for a. long period of time, and consequently tlie credit increment rate processes for the source stations are quasi-stationary. By using this quasi-sta.tiona.ry pro erty and by employing the techniques described in we are able to calc u h t e the steady-state system size distribution at the switch’s buffer, when the source stations are regulated by the Burst Level Feedback Scheme. To present this ca.lculation, we define the following variables.

111,

I,’,L:System size at. the network swit,ch at. the start. of‘ the 11-tll frallle; \;L= 0, I , 2 , , I,,,,,. ’ ’ ’

B;”:

Burst. duration index of the departure traffic from station 117 at. the start of the n-th franic?. See [ll]for its definition.

D!?’: The number of departing cells from station in during the n-th frame, LIP) = 0, 1, . . . , K . In [Ill, we show that this departure process

D(’”) =

{Dim),n 2 1) can be modeled as a Markov Modulat,ed Process (MMP) with BAm,”) as the modu1a.ti ng variable.

D,,: Total number of departing cells from M source st,ations during t,he wtli frame; i.e., D,, = E,”=,DL-,”);D, = 0, 1, 2 , ” . , M .I<. The system size process a.t, t,he buffer of the switch is governed by the following equa.tion:

where Y,,,,, is tlie capacity of the switch’s buffer and L is equal to the service rate a t the switch processor/trunks expressed in [cells/frame]. Using the quasist,ationary modeling assumption, we prescnt i n the following a solution technique for the evaluation of the steady-state behavior of the switch’s syslem size process.

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We define the steady-state joint distribution of the system-size process a t the switch and the burst duration indices of the M stations as:

ni,v

=

lim P(

n-cx,

B, = 6, Y,, =

y ),

(15)

)IA(R)I:number of inactive stations a t the start of a frame, given h.

To incorporate the burst-level status messages in the feedback information, we define:

where

B, = [ B p , B p ’ . . . , B y ) 3 (16) and -b = [ b ( I ) , b(2), . . . , b ( M ) 1. (17) To Analyze this feedback-based procedure, we consider next the performance of a system under which each station is regulated by a static CMA scheme which operates under a fised average credit increment. Given a fixed selection of the average credit increment vector h ( and the associated vector h defined below ), we set to denote the corresponding vector expressing the burst duration index at the start of the n-th frame. We then define

r

1

&

h(’n)= 0 , where

-

[

=

@1),

jp),..

. (

jl(W

1,

(19)

to denote the steady-state joint distribution of the system-size a t the swit.ch a,nd the modes of the A4 departure traffic strea.ms for a sta.t,ic credit increment rate system, wherein source station m’s credit is incremented by h.(”’), nz = 1, 2 , . . . , A4, = 1, 2,. . . , A’. To calculate the probabilities defined in Equation (18) using a. quasi-stat,iona.rymodeling approach, given a fised value for i.(m), ni 1, we assume station m t o be driven by a traffic stream which (depending on the value of is residing continuously in an active burst mode or in an idle burst mode. (Thus, no mode changes take place during the period under investiga.tion.) To differentiate t,hese conditions, we set, j,.(‘”) = 0 t,o designa.t,e a.n arrival process to station 772 which resides i n the “off (idle burst) mode. When an arrival process to station m resides in the “on” (active burst) mode, we set h(”’) = h(”). The values of h(’”) and h(m) are thus related as follows:

>

j-&m)

=

{

for

172

1

E IA(&) .

(22)

From the quasi-stationary modeling assumption, we then have:

By using Equations (22) and (23), and the solution technique presented in [ll] we obtain the steady-state distribution of the system size process a t the buffer of the switch. We then calcu1at.e the mean and t.he moments of the system size, and use Little’s Theorem to obtain the mean delay of a randomly selected cell. Since each station operates in a stable fashion, yielding a network average access rate which is lower than than 1 [ceIl/frame], we require L 2 M to ensure a stable operation of the switch’s queueing system when the switch’s buffer capacity is arbitrarily large. For a finite capacity switch buffer system, a stable (positiverecurrent) operation is always observed.

4

Performance Results

h(”a) when st,a.t,ionni is in “on” mode, 0

when st,at,ion 777. is in “off’mode. (20)

The following notations are defined. A ( @ : set containing ID’S of active stations, given i.e., A(&)=

{m:

ji(n1)

6;

> o}.

I A ( ~ )set : cont,aining ID'^ of inactive st8at,ions,given i.e., I A ( ~=) { m : ~ ( 9 1 1 ) = o . -i;

1

IA(&)I: number of active sta.tions a t the stmart.of a frame, given h.

In this section, we present a numerical esa.mplc to illust,rate the methodology developed in this paper. We also illustrate the conditions under which the Burst Level Feedback Scheme can improve the system’s performance, when compared with the performance achieved by using a static Credit. Manager .4 Igorithm Scheme. The system configuration for this emmple is depicted in Figure 3. Under this configuration, five source stations load a network switch. Each of the five source stations is regulated by the system’s Burst Level Feedback Scheme. The traffic process loading ea.ch of these five source sta.tions is assumed to be modeled as a IIlIa,rkov Modula.ted Process; when it is in the “on” mode, cell messages a.re

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generated in accordance with a geometric point process; when it is in the “off’ mode, no messages are generated. To examine t,he performance improvement t
=

G(”)

mean ‘‘off’ duration of the traffic streams mean “on” duration of the traffic streams a t station m a t station in

We set these indexes t o be the same for all 5 stations; i.e.,

G =

($1)

= G(2) = . . . = ( $ 5 ) .

(26)

For traffic st,reams of type-1, we set t.he burstiness index to be high, G( 1) = 4. For traffic streams of type2, we set this index to be relat,ively low, G(2) = 0.25. The average traffic intensities of these two traffic types are the same, X = 0.15 [cells/frame]. T h e mean arrival intensities of “on” and “off’ modes of these two traffic types are: X””(1) = 0.9, X””(2) = 0.225,

A ” f f ( 1) = 0; Aoff(2) = 0.

(27) (28)

Each station can be loaded by a traffic stream which is governed at the burst level by statistics described by the type-1 and type-2 burst streams defined above Given the loading stream to be in an idle ( “ o f f ) mode, no cell messages are generated. Given the loading stream t o be in an active (“on”) mode, cell-level arrival statistics are described as follows. Station 1 generates batch arrivals of size 20; stations 2 to 5 generate batch arrivals of size 8. For all stations, the elapsed time between successive credit increments is equal to 5 slots, A’ = 5. We set the maximum credit allowed at sta= 8, tions 2 t o 5 t o be equal t o 8, e$&= . . . = and study the performance variation as a function of em (1) ax.

T h e switch is assumed to have a service rate of

L = 5 [cells/frame] and a maximum buffer size of Y,,,,, = 30. We use these traffic and system config-

uratsion assumptions to examine the system’s performance under a Burst Level Feedback Scheme. T o verify our quasi-stationary assumption, we have also carried out a simulation study. When using our simulation model, we assume the network access switch to be located 10 kilometers away from the source stat.ions. A round-trip propagation delay of 100 p seconds is thus incurred by the feedback control messages. This delay represents the elapsed time from the instant at

which the source stations send their burst level information to the network switch t o the instant that the stations receive the system’s feedback (credit update) messages. In comparing our results (obtained through the use of the analytical quasi-stationary based model) with simulation results, we find these two methods to yield very close results. The simulation results are thus omitted. I n Figure 4, we present the performmce behavior experienced by a source sta.tion. W e show the mean syst,eni size level at, source sta.tion 1 as a. function of it,s e,,,,, value. T h e curves X1-H(FB) and X1-H(CMA) represent the mean system sizes of station 1 at its source buffer, when it is loaded by a highly bursty traffic streams (burst type-1), for which G = 4 . The other source stations are also loaded by the highly bursty type-1 streams. We examine separately two regulation schemes which are applied to all stations: the Burst Level Feedback Scheme (FB) and the Credit Manager Algorithm (CMA). We observe that the mean system size a t station 1 is drastically reduced when the Burst Level Feedback Scheme is used t o regulate traffic. U n der highly bursty traffic loading, the probability that a.ll 5 sta.tions simultaneously reside in an active burst, mode is low. Hence, the feedback scheme can then effect.ively distribute extra credit to the active stations. As a result, we observe that the mean system size of station 1 is reduced substantially by the use of the Burst Level Feedback Scheme. T h e curves X1-L(FB) and Xl-L(CMA) represent the mean system sizes of station 1 when it and the other stations are loaded by the less bursty (type-2) streams, G = 0.25, and when the source stations are regulated by the Burst Level Feedback Scheme and the Credit Manager Alorit,hm, respectively. Under such relatively uniform $1 ess bursty) traffic loading conditions, we observe, as expected, that the feedback burst-level iiifortiialioii does not lead t o a distinct performance improvement,. I n Figure 5, we present the net,work swit,ch performance. We examine the mean system size a,t the switch’s buffer as a function of the C,,,,, value at station/l. We note that the cures SW-H(FB) and SW-H(CMA) represent the mean system sizes a t the switch when highly bursty traffic streams, G = 4 , are used to load the source st,ations, and when the stat>ions are regulated by the Burst Level Feedback Scheme a.nd the Credit, Manager Algorithm, respectively. Notme that under the Feedback Scheme, the switch’s service resources are used more effectively, leading to an increase in the burstiness of the stations’ regulated departing processes. As a result,, an increase in the switch’s system-size level is expected. We find the increase in the n1ea.n system size a t the network switch due to the use of the Burst Level Feedback Scheme t.o be rather minimal. Thus, the cell delay a t the switch under the Burst Level Feedback Scheme is not highly increased. T h e curves SW-L(FB) and SW-L(CMA) represent the mean syst.em sizes a t the switch when low bursty traffic streams, G = 0.25, are used t o load the source stations, and when the stations are regulated by the Burst Level Feedback Scheme and the Credit Manger Algorithm, respectively. We observe that, as expected, they yield the same mean system-

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size levels a t the switch’s buffer. In Figure 6 , we now use a simulation program to obtain the cell loss probabilities at the buffer of the network’s switch. The curves FB-40 and CMA-40 represent the cell loss probabilities at the switch’s buffer, when highly bursty traffic streams, G = 4, are used to load the source stations, when the maximum credit allowed a t station 1 is 40, C,(& = 40, and when the source stations are regulated by the Burst Level Feedback Scheme and the Credit Manager Algorithm, respectively. We observe only a slight increase in the cell loss probability under the use of the Burst Level Feedback Scheme. The curves FB-10 and CMA-10 represent the cell loss probabilities at the switch’s buffer, when highly bursty traffic streams, G = 4, are used to load the source stations, when the maximum credit allowed a t station 1 is 10, C;!,’, = 10, and when the source stations are regulated by the Burst Level Feedback Scheme an the Credit Manager Algorithm, respectively. Now, due to the reduction in the C m a z ( l ) level, the st,at,ions’ regulated departing processes a.re less bursty. As a result, lower blocking probability levels are attained. In compa.ring the CMA and the Burst Level Feedback Scheme, again only a small difference in blocking probability performance is observed. By using Little’s theorem, we obtain the end-toend mean cell delay, representing the average end-toend delay incurred by a cell, consisting the cell’s delay at its source station plus its delay at the network switch. This mean delay is calculated for a randomly select,ed cell, under various regulation levels as shown in Figure 7. The curves D-H(FB) and D-H(CMA) represent the mean end-to-end cell delay when highly bursty traffic streams, G = 4, are used to load the source stations, and when the source stations are regulated by the Burst Level Feedback Scheme and the Credit Manager Algorithm, respectively. We observe that the mean end-to-end delay of a randomly selected cell is greatly reduced under the use of the Burst Level Feedback Scheme. This performance improvement is attributed to the stochastical multiplexing gain afforded through the use of the Burst Level Feedback Scheme. The curves D-L(FB) and D-L(CMA) represent the mean end-to-end delay of a randomly selected cell when low bursty traffic streams, G = 0.25, are used t o load the source stations, and when the source stations are regulated by the Burst Level Feedback Scheme and the Credit Manger Algorithm, respectively. We observe now the two schemes to yield the same delay levels. This is expect>edto be the case when the underlying loading traffic streams are less bursty. Comparing Figures 4, 5, 6, and 7, we conclude that the Burst Level Feedback Scheme can improve the system performance drastically when the system is loaded by highly bursty traffic. As shown in these Figures, the mean system sizes at the source stations and the mean end-to-end delay of a randomly selected cell are both greatly reduced under highly bursty loading situation, when the Burst Level Feedback Scheme is used to regulate the traffic flows. Only minimal increases in the switch’s queue-size levels and in the blocking

probabilities at the switch’s buffer are observed. Coiisequently, the burstiness embedded in traffic flows fed by the source stations to the network’s switch is controlled. As shown in these Figures, the system performance is significantly improved under highly bursty tra.ffic loading situation, as is typically the case in t,he traffic characteristics of ATM supported services. Our research results provide an analytical tool for the investigation and study of such related performance issues.

5

Conclusions

In this paper, we have introduced and studied a new input rate flow control meclianisni, the Burst Level Feedback Scheme. Burst level information is used to gain performance improvement. We also present. an analytical methodology for the analysis and perforinance evaluation of this scheme. Performance results are shown to illustrate the features of the analytical technique developed in this paper and to demonstrate the performance improvement obtained by the Burst Level Feedback Scheme. We show this input rate control scheme to be effective for traffic regulation at the access to an ATM network loaded by highly bursty stations. The analytical tools developed here allow the system designer to evaluate the proper level of input regulation that should be used to guarantee acceptable queue-size and delay levels at the source station’s buffer and at the buffer of the shared network switch.

References Hamid Ahmadi, Roch GuCrin, and Khosrow Sohraby, “Analysis of Leaky Bucket Access Control Mechanism with Batch Arrival Process”; Proceedings of I E E E G L O B E C O M Conference, San Diego, CA, 1990. Krishna Bala, Israel Cidon, and Khosrow Sohraby, “Congestion Control for High Speed Packet Switched Networks”; Proceedtngs of I E E E INFOCOM Conference, San Francisco, CA, 1990. P. Boyer, J . Boyer, and J . R . Louvion, “Sproadic Flows in an Asynchronous Time-Division Network”; COST 214, doc. 061, Aug. 1986. Milena Butt6, Elisa Cavalero, and Albert0 Tonietti, “Effectiveness of the Leaky Bucket Policing Mechanism in ATM Networks”; I E E E Journal on Selected Areas in Comiiiuntcataoiis, Vol. 9, No. 3, April 1991. Israel Cidon and Inder Glopal, “PARIS: In Approach to Intergrated High Speed Private Networks”; Proceedings of International Journal on Digital and Analog Cabled S y s t e m s , Vol. 1, 1988.

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Israel Cidon and Inder S. Gopal, “Control Mechanisms for High Speed Networks”; Proceedings of ZEEE Znternational Conference on Communications (ZCC), April 1990.

Figure 1 I l l u s t r a t i o n o f a s t a t i c Credit Manager Algorithm Cell A r r i v a l s

Transm it t e r

[7] Anwar I. Elwalid and Debasis Mitra, “Stochastic Fluid Models in the Analysis of Access Regulation in High Speed Networks”; Proceedings of I E E E G L O B E C O M Conference, Phoenix, AZ, 1991. [SI Kin K. Leung, Bhaskar Sengupta, and Raymond W. Yeung, “Queueing Analysis of a Credit Manager for Flow Control of High Speed Networks”; Proceedings of I E E E ZNFOCOM Coiiference, 1992.

t

Cell B u f f e r

Credit Buffer

[9] Izhak Rubin and I<. David Lin, “Queueitig Behavior under Flow Control at t,he Subscriber-toNetwork Interface for High Speed Metropolitan Area Networks”; Proceedings of I E E E I N F O C O M Conference, Florida, April 1991.

[lo]

Izhak Rubin and I<. David Lin, “Input Rate Flow Control for High-speed Networks: Source vs. Switch Level Performance Trade-off’ ; Proceedliiya of I E E E G L O B E C O M Conference, Arizona, December 1991.

[ll] Izhak Rubin and I<. David Lin, “Input Rate Flow Control for High-speed Networks: Blocking and Delay a t the Access Points”; U C L A Technical Report, University of California, Los Angeles, January 1992.

I Figure 2 Queueing models

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Buff er5

Rate F l o w Contro 1 1 ed Servers

Arrivals

1

[12] Izhak Rubin and K. David Lin, “Performa.nce Evaluations of Three Input. Rate Control Schemes”; Proceedings of Iiiteriiutioiral Confere ii ce on C o m put e r C o 111 mu it,icu 1.io 1t.s a ii d hlc t works, San Diego, Ca.lifornia, June, 1992. [13] Khosrow Sohraby mid Moshe Sidi, “On the Performance of Bursty and Correhted Sources Subject. t,o Leaky Bucket. Ra.te-Based access Coiit.ro1 Schemes”; Proceedings of I E E E IhlFOCOill Coirferencc, Florida., April 1991.

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A r r iv a 1s

Network Switch

M

[14] K. Sriram a.nd W. Whitt, ‘Cha,racterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Da.ta.”; I E E E Journal on Selected Areas an Commiinicatiolrs, Vol. SAC-4, No. 6 , September 1986.

Source S t a t i o n s

[15] William St,allings, Da2a and Coinputer COInl7l unications; Macmillan Publishing Company. New York, 1985, 1988. [ l G ] Geiieric S y s t e m Requireineiit in Supports of Switched Mulfi-megabit D a t a Sertltce; Bellcore TA-TSY-000772, Issue 2, March 1989.

Credit Generator

Flgure 3 Test system conflguratlon

MMP

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L=5

Station 4

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Figure 4 Source Station Performance

Figure 6 End-to-End Delay Performance 61

4 1

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50 20

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Cmax(1)

X1-H(CMA): CMA station with High Bursty Traffic Xl-H(FE): FE station with High Bursty Traffic Xl-L(CMA): CMA station with Low Eursty Traffic X1-L(FB): FE station with Low Bursty Traffic

Figure 5

10

0

Cmax(1)

D-H(CMA): High Eursty Traffic 8 CMA stations D-H(FE):High Eursty Traffic 8 FB stations D-L(CMA):Low Eursty Traffic 8 CMA stations D-L(FE):Low Eursty Traffic 8 FE stations

Switch Performance

-Figure 7 Switch Blocking Performance

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SW-L(CMA) 8 SW-L(FB) J

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SW-L(CMA):Low Bursty Traffic from CMA stations SW-L(FB):Low Bursty Traffic from FB stations SW-H(CMA):High Bursty Traffic from CMA stations SW-H(FB):High Bursty Traffic from FB stations

14

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, 18

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FB-40: FB stations with Cmax(l)=40 CMA-40: CMA stations with Cmax(l)=40 FB-10: FE station with Cmax(l)=lO CMA-10: CMA station with Cmax(l)=lO

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