Lecture 12

# N 21 x 2 nq 2 2 x 2 21 1 t w another

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Unformatted text preview: -exponential server, inﬁnite population So far, we have considered exponential server case. However, the service distribution could be nonexponential. Thus, results for non-exponential service time are also desirable. There are several results for this one; however, the mathematical derivation is quite complex and beyond the scope of this course. As such, we list a couple of results for M/G/1 system below: W  = 21X  , 2 where X 2 is the second moment of the service time distribution. N  = + 21 X  : , 2 Nq = 2 2 X 2 21 ,  : 1 T = + W:  Another important special case of M/G/1 (besides M/M/1) is M/D/1, i.e., the service time is deterministic. The deterministic service time is applicable, for example, in ATM (Asynchronous Transfer Mode) networks where cell size are ﬁxed and thus service rate is ﬁxed (we will address at some point later whether Poisson arrival is a good assumption for ATM trafﬁc, or for other networks such as Internet). Results for M/D/1 are listed below: = 21 ,  2, T= 21 ,  W N 2 = + 21 ,  Nq = 2 21 ,  : 19. G/M/1 and G/G/1 G/M/1 refers to the case where the inter-arrival time is non-exponential while the service...
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## This document was uploaded on 03/19/2014 for the course CS 6030 at Western Michigan.

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