On queues with service and interarrival times depending on waiting times

We consider an extension of the standard G/G/1 queue, described by the equation W D = max{0, B − A + Y W}, 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.

• Type: Journal
• Year: 2007
• Where: QUESTA
• Authors: Onno J. Boxma, Maria Vlasiou
• Keywords: Classical Lindley Equation, Model, QUESTA 2007, Standard