Work

On queues with service and interarrival times depending on waiting times

Year: 2007

Type: article

Abstract: We consider an extension of the standard G/G/1 queue, described by the equation $W\stackrel{ \mathcal {D}}{=}\max\mathrm{max}\,\{0,B-A+YW\}$ , 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.

Source: Queueing Systems

DOI: 10.1007/s11134-007-9011-3

Authors: O. J. Boxma, M. Vlasiou

Institutions: Eindhoven University of Technology, Georgia Institute of Technology

Language: English

Topic: Advanced Queuing Theory Analysis

Subfield: Management Information Systems

Field: Business, Management and Accounting

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

OpenAlex ID: W2107233141