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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

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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

Iyindex 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:) 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

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 tions 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