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On the mean sojourn time of jobs in queues by general service disciplines

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  01 July 2016

Gunter Ritter
Gunter Ritter*
Affiliation:
Universität Passau
*
* Postal address: Fakultät für Mathematik und Informatik, Universität Passau, 94030 Passau, Germany.
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Abstract

Existence and finiteness of the sample-mean limit of sojourn times of jobs in a queueing system are investigated. The queueing system operates under rather general multiprocessor disciplines allowing job classes and priorities. The input stream of jobs consisting of job classes and interarrival and processing times is stationary and ergodic and may contain batch arrivals. Existence of the sample-mean limit is proved by means of the superadditive ergodic theorem, and its finiteness is controlled by uniform mixing of the input stream.

Keywords

QUEUEING SYSTEMSSTATIONARY AND ERGODIC INTERARRIVAL AND PROCESSING TIMESG/G/mG/G1/mBATCH ARRIVALSGENERAL MULTIPROCESSOR DISCIPLINESJOB CLASSESPRIORITIESWORK CONSERVATIONSOJOURN TIMEWAITING TIMESUPERADDITIVE ERGODIC THEOREMUNIFORM MIXING

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 26 , Issue 2 , June 1994 , pp. 516 - 538
Copyright
Copyright © Applied Probability Trust 1994 

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