TY - JOUR

T1 - On queues with service and interarrival times depending on waiting times

AU - Boxma, O.J.

AU - Vlasiou, M.

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

U2 - 10.1007/s11134-007-9011-3

DO - 10.1007/s11134-007-9011-3

M3 - Article

VL - 56

SP - 121

EP - 132

JO - Queueing Systems: Theory and Applications

JF - Queueing Systems: Theory and Applications

SN - 0257-0130

IS - 3-4

ER -