By Ravi Mazumdar, Jean Walrand
This monograph offers a concise mathematical technique for modeling and reading the functionality of conversation networks with the purpose of figuring out the phenomenon of statistical multiplexing. the newness of the monograph is the clean process and insights supplied by way of a sample-path technique for queueing types that highlights the real rules of Palm distributions linked to site visitors types and their function in functionality measures. additionally provided are fresh principles of huge buffer, and plenty of assets asymptotics that play a major position in realizing statistical multiplexing. specifically, the $64000 notion of powerful bandwidths as mappings from queueing point phenomena to loss community versions is obviously awarded in addition to a close presentation of loss community types and exact approximations for giant networks. desk of Contents: advent to site visitors types and research / Queues and function research / Loss types for Networks / Statistical Multiplexing
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Additional info for Performance Modeling, Loss Networks, and Statistical Multiplexing (Synthesis Lectures on Communication Networks)
Sample text
Most switches have servers that work at a constant rate in which case the service time distribution is the packet length distribution. If it is M, it implies that the service times are exponentially distributed. d. with distribution G(t). If it is G, then the service times are identically distributed with distribution G(t) but need not be independent. Many books do not differentiate between GI and G. 3. C denotes the number of servers. Typically, C = 1 or some integer and could be infinite. 4. K denotes the total number of places in the system.
20 INTRODUCTION TO TRAFFIC MODELS AND ANALYSIS the limits exist): P(A) = PN (A) = t 1 t→∞ t lim 1I(θs ◦ ω ∈ A)ds 0 1 t→∞ Nt t lim 1 t→∞ Nt Nt 1I(θs ◦ ω ∈ A)dNs = lim 0 1I(θTk ◦ ω ∈ A) k=1 where we have used definition of the Stieltjes integral in the last step. )? To better understand this issue let us first study it in the discrete-time setting. The interpretation of θs ◦ ω is that of a sample point at time s. Let {ξn } be a stationary sequence (identically distributed) of random variables taking values in {0, 1}.
8 Let Qt be the congestion process resulting from a stationary arrival process At and a corresponding departure process Dt . , πA (n) = πD+ (n), n = 0, 1, 2, . . ) denotes the distribution just after the departure. Moreover, if the queue is of the M/G/1 type then: πD+ (n) = π(n), n = 0, 1, 2, . . where π(n) is the stationary distribution of the queue. In the general case, it is of interest to compute quantities under the stationary distribution. For stationary (and ergodic) single server queues, there is a very simple relationship that can be found in terms of so-called conditional intensities that we develop below.