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Queueing Behavior under Flow Control at the Subscriber-to-Network Interface for High Speed Metropolitan Area Networks Izhak Rubin and K. David Lin Department of Electrical Engineering, Engineering IV,56- 125B University of Califomia, Los Angeles, Los Angeles, CA 90024

Abstract A Credit Manager Algorithm (CMA) is used to control the flow of packets between a subscriber station ( or a local area network ) and the access to a high-speed metropolitan area network. The parameters of the algorithm are used to regulate the mean throughput and the level of burstiness at the Subscriber-to-Network Interface (SNI). Such a flow control procedure has been recently considered by the BELLCORE'S Switched Multimegabit Data Service (SMDS). We study the queueing behavior induced by such a flow control scheme. We examine the increased queue size and message delays incurred at the subscriber's station buffer due to the controlled access mechanism, as a function of the underlying system parameters. We also investigate the statistics of the output process by characterizing it as evolving among idle, burst, and restricted modes. We present performance curves illustrating the behavior of the station queues and of the regulated output traffic streams. 1. Introduction For many communication networks, conventional end-to-end window flow control schemes can yield unsatisfactory delay-throughput performance trade-off and exhibit fairness problems. These problems are becoming more significant as the speed of transmission increases and the statistical variations of the mixed-services offered traffic grow. For high speed networks, it is important to have a different flow control mechanism to ensure acceptable performance. The concept of input rate control, so-called "leaky-bucket" method, was employed in [2][3]. The performance behavior of such a method is critically dependent upon the bursty nature of the offered traffic. In the IBM's PARIS[4] experimental packet switched network, an "input throttle" procedure has been adopted to regulate traffic. A queueing model is presented in [5] to analyze this scheme. The analysis presented in the latter paper assumes zero packet transmission times and the same token ( credit )

requirement for all packets, independent of their packet lengths. A general flow control scheme employing the Credit Manager Algorithm has been presented by Bellcore[ 11 to administrate the traffic at the subscriberto-network interface (SNI) for high speed Metropolitan Area Networks. Such an algorithm regulates the admission of traffic at the SNI, allocating different access parameters to different access classes. On the customer premises equipment (CPE) side, the credit manager algorithm protects the customers from being overflowed by the network; therefore, they need not allocate extra resources at the interfaces. On the other hand, network providers have to provide only the actual required resources to buffer the incoming traffic. The credit manager algorithm is implemented in the SMDS Interface Protocol ( SIP ) at layers SIP2 and SIP3 [l]. At both the CPE and the MSS ( MAN Switching System ) access points, the system has to transmit and accept data in accordance with the algorithm, as summerized in the following. For the transmission of a SIP packet, the system has to acquire sufficient credit, depending on the size of the packet, before it can be accommodated. A basic entity, of a prescribed length, called an Information Unit (IU)is defined. Each packet can contain multiple Ius. The system checks the number of Information Units contained in each level 3 Protocol Data Unit ( L3-PDU ), compares it with current available credit, and determines whether to let the packet pass through the SNI or delay it. The system then subtracts the required credit used for the packet from the total available credit, if the packet is accepted for transmission, and then it proceeds to transmit the packet across the SNI. The available credit is incremented by one every At seconds, noting that the maximum credit value allowed is equal to the upper limit Cma. Assume each Information Unit to contain p bits and the transmission rate of the link to be v bits per second. The average throughput across the SNI is set to correspond to the transmission of p bits every Af seconds. This rate is designated as the Sustained Access Rate (SAR). The maximum number of bits that can be transmitted when credit reaches C ,, defined as MAXBURST, can be expressed as 161 :

4C.2.1. 0382

CH2979-3/91/0000-0382 $1 .OO

0 1991 IEEE

Authorized licensed use limited to: Univ of Calif Los Angeles. Downloaded on March 4, 2009 at 01:06 from IEEE Xplore. Restrictions apply.

containing L segments ) every K slots, so that SAR

L1

where x denotes the maximum integer not greater than x . Equahon (1.1) can be simplified to yield equation (1.3) when condition (1.2) is met :

x,

CnUlXO 1

%j,k =ai

n0J.k-1

+

am n i - m + l j + l , k - l md)

C ,,

(5.6)

n=O

(b) For c,,

{

> j > 0, K - 1 2 k > 0

(5.16)

j z 0,

P (Xatl= i, C.,l=j,N.+1= k )=ail' (X.= 0, C.=j,N.= k-1 )

+ ~u,P(X.=i-m+l,C,=j+I,N.=k-l).

(5.7)

m=O

= c,

(c) For j

P(X.+l=i,C.+l=C,fln+l=k

(5.8)

)=u,P(X,=O,C.=C,,~"=k-l).

j=l,k=O

(5.19)

C,>j>l,k=O

(5.20)

Case (B) N . , ~= k = o : (a) For c.+~ = j = 0, P ( Xn+l= i, c.+1=0, Nn+l=0 ) = 0.

(b) For

(5.9)

=j = I ,

P ( Xn+l=i , Cn+l=~ , I V . , ~ =0 ) = Ccq,,f(X.= i-m, C.=O,N.= K-1 ) *=O

+ Zu,P

(X.= i-m+l,c.= 1,N.= K-l ) .

+

(5.10)

C a m Ri-m+1,CmUp-l

Cmax=j* k = O . (5.21)

m=O

m a

(c) For c,,

This set of linear equations can be numerically solved, under the boundary condition :

> j z 1,

P ( Xntl= i , Cn+l=j , N.+,= 0 ) = u i P (X.= 0, C.= j - 1 , N,,= K-1 )

00

cmu

C Cx( i , j I + Cu,f(X.=i-m+l,C.=j,N.=K-l).

(5.11)

n=O

(d) For j = c,,, P (Xntl= i,C.+l=C,,N.,l=O)=uiP

+ UiP (X.= + C u,P

0, c.= C--L

(X.=O,C,=C,,,N.=K-l)

N,= K - 1 )

m=O

The steady-state conditional probabilities, when they exist, are given by : n i j k EX(

(5.13)

i, j I k ) = "+ l i m f ( X . = i , C . = j , IN,, = k ) ,

The joint steady-state distribution of (xn, C. given by :

)

is then

for each k , 0 Ik I K - 1

. (5.22)

A computer program based on Gauss-Seidel method has been used to solve these equations, under a properly truncated state space. To illustrate performance, a geomemc-batch arrival process is considered. Packets arrive in batches in accordance with a geometric point process; each batch consists of B packets, B > 0. Then we have :

(5.12)

(X.= i-m+l, C.= C,,, N.= K-1 ) .

k ) = 1,

i=O j=O

U,,,=

I

p , I-p, 0,

h=C mma,=Bp

m=B m=O

(5.23)

otherwise

,

B>O,O