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M/M Infinite Service System with Ranked Servers in Heavy Traffic : Lecture Notes in Economic and Mathematical Systems - Gordon Frank Newell

M/M Infinite Service System with Ranked Servers in Heavy Traffic

Lecture Notes in Economic and Mathematical Systems

By: Gordon Frank Newell, Franz Ferschl (Introduction by)

Paperback

Published: October 1984
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We are concerned here with a service facility consisting of a large (- finite) number of servers in parallel. The service times for all servers are identical, but there is a preferential ordering of the servers. Each newly arriving customer enters the lowest ranked available server and remains there until his service is completed. It is assumed that customers arrive according to a Poisson process of rate A , that all servers have exponentially distributed service times with rate ~ and that a = A/~ is large compared with 1. Generally, we are concerned with the stochastic properties of the random function N(s ,t) describing the number of busy servers among the first s ordered servers at time t. Most of the analysis is motivated by special applications of this model to telephone traffic. If one has a brunk line with s primary channels, but a large number (00) of secondary (overflow) channels, each newly arriving customer is assigned to one of the primary channels if any are free; otherwise, he is assigned to a secondary channel. The primary and secondary channels themselves could have a preferential ordering. For some purposes, it is convenient to imagine that they did even if an ordering is irrelevant.

1. Introduction.- 2. Limit properties for a " 1.- 3. Descriptive properties of the evolution.- 4. The overflow distribution.- 5. Joint distributions.- 6. A diffusion equation.- 7. Transient properties.- 8. Equilibrium properties of the diffusion equation.- 9. Equivalent random method.- Index of Notation.

ISBN: 9783540133773
ISBN-10: 3540133771
Series: Lecture Notes in Economic and Mathematical Systems
Audience: General
Format: Paperback
Language: English
Number Of Pages: 129
Published: October 1984
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 24.41 x 16.99  x 0.79
Weight (kg): 0.24