Abstract
We consider an extension of the standard G/G/1 queue, described by the equation , 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.
Original language | English |
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Pages (from-to) | 121-132 |
Journal | Queueing Systems |
Volume | 56 |
Issue number | 3-4 |
DOIs | |
Publication status | Published - 2007 |