Analysis of M/G/1-queues with Setup Times and Vacations under Six Different Service Disciplines

  • Single server M/G/1-queues with an infinite buffer are studied; these permit inclusion of server vacations and setup times. A service discipline determines the numbers of customers served in one cycle, that is, the time span between two vacation endings. Six service disciplines are investigated: the gated, limited, binomial, exhaustive, decrementing, and Bernoulli service disciplines. The performance of the system depends on three essential measures: the customer waiting time, the queue length, and the cycle duration. For each of the six service disciplines the distribution as well as the first and second moment of these three performance measures are computed. The results permit a detailed discussion of how the expected value of the performance measures depends on the arrival rate, the customer service time, the vacation time, and the setup time. Moreover, the six service disciplines are compared with respect to the first moments of the performance measures.

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Metadaten
Author:Wolfgang Bischof
Parent Title (English):Queueing Systems: Theory and Applications (QUES)
Publisher:Springer US
Document Type:Contribution to a Periodical
Language:English
Publication Year:2001
Tag:M/G/1-queues with setup times and vacations; Service disciplines; Waiting time; queue length
Volume:39
Issue:4/2001
First Page:265
Last Page:302
faculties / departments:Fakultät für Angewandte Natur- und Geisteswissenschaften
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik