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Distribution of the workload in multiclass queueing systems with server vacations
Author(s) -
Takagi Hideaki,
Takine Tetsuya,
Boxma Onno J.
Publication year - 1992
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(199202)39:1<41::aid-nav3220390104>3.0.co;2-k
Subject(s) - workload , switchover , computer science , polling system , queueing theory , real time computing , poisson distribution , polling , service (business) , computer network , distributed computing , operating system , mathematics , statistics , economy , economics
The steady‐state workload at an arbitrary time is considered for several single‐server queueing systems with nonpreemptive services for multiple classes of customers (arriving according to Poisson processes) and server vacation (switchover) times. The distribution of the workload at an arbitrary point during the vacation period is obtained for systems with setup times, and for polling systems with exhaustive, gated, or globally gated service disciplines. From the stochastic decomposition property, this workload is added to the workload in the corresponding M/G/1 system without vacations to give the workload at an arbitrary time in vacation systems. Dependence of the workload distribution on the vacation parameters is studied.