This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Computer Networks M/M/1 with finite queue Saad Mneimneh Computer Science Hunter College of CUNY New York Sorry, I have to drop you! 1 Introduction We now reexamine the M/M/1 queing system under the more realistic assump tion of a finite queue size. Therefore, we assume that the queue can hold up to m packets. If a packet arrives and the queue is full, the packet is simply dropped from the system. The analysis of M/M/1 under this setting will give us some insight into the behavior of networks in general, and an idea for a congestion control algorithm used by TCP. 2 The Markov chain For this new setting, we have a finite Markov chain with a set of states { , 1 , 2 ,...m } and transional probabilities as illlustrated in Figure 1. As before, we need to find the steady state probability p n of being in state n (system has n packets). The steady state equations are as follows (refer to Figure 1): p = p (1 ) + p 1 + o ( ) p m = p m 1 + p m (1 ) + o ( ) p n = p n 1 + p n (1  ) + p n +1 + o ( ) n 6 = 0 ,m 1 1 2 m m1 1  1  1  1 1 Figure 1: Markov chain for finite M/M/1 m X n =0 p n = 1 Since lim o ( ) / = 0, taking the limit as goes to 0 gives: p n p n 1 = = Therefore, m X n =0 p n = 1 m X n =0 n p = 1 p = 1...
View
Full
Document
 Spring '08
 SaadMneimneh
 Computer Networks

Click to edit the document details