Overview

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.

Full Product Details

Author:   G.F. Newell ,  F. Ferschl
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of the original 1st ed. 1984
Volume:   231
Dimensions:   Width: 17.00cm , Height: 0.70cm , Length: 24.40cm
Weight:   0.262kg
ISBN:  

9783540133773

ISBN 10:   3540133771
Pages:   129
Publication Date:   01 September 1984
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

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.

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