An Exact Solution for an M(t)/M(t)/1 Queue with Time-Dependent Arrivals and Service

Authors:
Charles Knessl;Yongzhi Peter Yang
Affiliations:
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607-7045, USA, , Department of Mathematics, University of St. ...;Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607-7045, USA, , Department of Mathematics, University of St. ...
Venue:
Queueing Systems: Theory and Applications
Year:
2002

Citing 4
Cited 3

Testing the validity of a queueing model of police patrol

Management Science
The Fourier-series method for inverting transforms of probability distributions

Queueing Systems: Theory and Applications - Numerical computations in queues
Asymptotic analysis of the M/G/1 queue with a time-dependent arrival rate

Queueing Systems: Theory and Applications
A sample path analysis of the M_t/M_t/c queue

Queueing Systems: Theory and Applications

Fundamental characteristics of queues with fluctuating load

SIGMETRICS '06/Performance '06 Proceedings of the joint international conference on Measurement and modeling of computer systems
Asymptotically Optimal Controls for Time-Inhomogeneous Networks

SIAM Journal on Control and Optimization
Fitting the Pht/Mt/s/c Time-Dependent Departure Process for Use in Tandem Queueing Networks

INFORMS Journal on Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider an M/M/1 queue with a time dependent arrival rate λ(t) and service rate μ(t). For a special form of the traffic intensity, we obtain an exact, explicit expression for the probability pn(t) that there are n customers at time t. If the service rate is constant (=μ), this corresponds to ρ(t)=λ(t)/μ=(b−aμt)−2. We also discuss the heavy traffic diffusion approximation to this model. We evaluate our results numerically.