# Approximate Behavior of Tandem Queues

• Gordon F. Newell
Book

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 171)

1. Front Matter
Pages N2-XI
2. Gordon F. Newell
Pages 1-42
3. Gordon F. Newell
Pages 43-89
4. Gordon F. Newell
Pages 90-148
5. Gordon F. Newell
Pages 149-217
6. Gordon F. Newell
Pages 218-230
7. Gordon F. Newell
Pages 231-312
8. Gordon F. Newell
Pages 313-380
9. Gordon F. Newell
Pages 381-402
10. Back Matter
Pages 403-413

### Introduction

The following monograph deals with the approximate stochastic behavior of a system consisting of a sequence of servers in series with finite storage between consecutive servers. The methods employ deterministic queueing and diffusion approximations which are valid under conditions in which the storages and the queue lengths are typically large compared with 1. One can disregard the fact that the customer counts must be integer valued and treat the queue as if it were a (stochastic) continuous fluid. In these approximations, it is not necessary to describe the detailed probability distribution of service times; it suffices simply to specify the rate of service and the variance rate (the variance of the number served per unit time). Specifically, customers are considered to originate from an infinite reservoir. They first pass through a server with service rate ~O' vari­ ance rate ~O' into a storage of finite capacity c . They then pass l through a server with service rate ~l' variance rate ~l' into a storage of capacity c ' etc., until finally, after passing through an nth server, 2 they go into an infinite reservoir (disappear). If any jth storage become , n , the service at the j-lth server is interrupted full j = 1, 2, and, of course, if a jth storage becomes empty the jth server is inter­ rupted; otherwise, services work at their maximum rate.

### Keywords

Distribution Image Queues Warteschlange equilibrium evaluation merger probability probability distribution science and technology service value-at-risk

#### Authors and affiliations

• Gordon F. Newell
• 1
1. 1.Institute of Transportation StudiesUniversity of CaliforniaBerkeleyUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-46410-2
• Copyright Information Springer-Verlag Berlin Heidelberg 1979
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-540-09552-1
• Online ISBN 978-3-642-46410-2
• Series Print ISSN 0075-8442
• Buy this book on publisher's site
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