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On Regenerative Processes in Queueing Theory

Name: On Regenerative Processes in Queueing Theory
Brand: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
SKU: 06623465
Price: 51.68 EUR
Availability: InStock
Author: Jacob Willem Cohen
ISBN: 9783540076278

Jacob Willem Cohen

Language

English

Book Paperback

Libristo code: 06623465

Publishers Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, March 1976

I. The single server queue GIIG/1 1 1. 1 Definitions 1 1. 2 Regenerative processes 2 1. 3 The sequen... Full description

Libristo code: 06623465

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I. The single server queue GIIG/1 1 1. 1 Definitions 1 1. 2 Regenerative processes 2 1. 3 The sequence n 1,2, . . . 4 = !::!n' 1. 4 The process t dO,co)} 11 {~t' The process t dO,co)} 1. 5 15 {~t' Applications to the GIIG/1 queue 1. 6 16 The average virtual waiting time during a busy 17 cycle ii. Little's formula 17 iii. The relation between the stationary distributions 18 of the virtual and actual waiting time iv. The relation between the distribution of the idle 20 period and the stationary distribution of the actual waiting time v. The limiting distribution of the residual service 24 time Pds. . , -pw vi. The relation for ~ rn E{e -n} 25 n=O 1. 7 Some notes on chapter I 27 II. The M/G/K system 31 2. 1 On the stationary distribution of the actual and virtua131 waiting time for the M/G/K queueing system 2. 2 The M/G/K loss system 36 2. 3 Proof of Erlang's formula for the M/G/K loss system 43 i. Proof for the system MIMI'" 45 ii. Proof for the system M/G/co 47 VI iii. Proof fol' the MIG IK los s system III. The M/G/1 system 3. 1 Introduction 71 (K) 3. 2 Downcrossings of the ~t -process 74 3. 3 The distribution of the supremum of the virtual waiting 75 (00) d' b 1 tlme ~t urlng a usy cyc e i. The exit probability 76 ii.