Title :
The transient solution of time-dependent M/M/1 queues
Author :
Zhang, Ji ; Coyle, Edward J., Jr.
Author_Institution :
Rensselaer Polytech. Inst., Troy, NY, USA
fDate :
11/1/1991 12:00:00 AM
Abstract :
The transient behavior of time-dependent M/M/1 queues is studied. The boundary probability function π0(t), which is the probability that the queue is empty at time t, is shown with analyticity arguments to satisfy a Volterra-type integral equation. The boundary integral equation is derived, and a numerical algorithm is used to solve the integral equation and to find the expected queue size from π0(t). The approach can be applied to many other types of time-dependent queues. Examples are given
Keywords :
integral equations; queueing theory; transient response; Volterra-type integral equation; boundary integral equation; numerical algorithm; oundary probability function; time-dependent M/M/1 queues; transient behavior; Approximation methods; Difference equations; Differential equations; Integral equations; Iterative methods; Linear systems; Manufacturing; Markov processes; Partial differential equations; Queueing analysis;
Journal_Title :
Information Theory, IEEE Transactions on
