期刊
QUEUEING SYSTEMS
卷 56, 期 3-4, 页码 121-132出版社
SPRINGER
DOI: 10.1007/s11134-007-9011-3
关键词
Lindley recursion; G/G/1 queue; Alternating service model
We consider an extension of the standard G/G/1 queue, described by the equation W-D/=max{0,B-A+YW} where P[Y=1]=p and P[Y=-1]=1-p. For p=1 this model reduces to the classical Lindley equation for the waiting time in the G/G/1 queue, whereas for p=0 it describes the waiting time of the server in an alternating service model. For all other values of p, this model describes a FCFS queue in which the service times and interarrival times depend linearly and randomly on the waiting times. We derive the distribution of W when A is generally distributed and B follows a phase-type distribution, and when A is exponentially distributed and B deterministic.
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