Mt/G/∞ queues with sinusoidal arrival rates
Management Science
On the transient behaviour of the Erlang loss model: heavy usage asymptotics
SIAM Journal on Applied Mathematics
The physics of the Mt/G/ ∞ symbol Queue
Operations Research
Strong approximations for time-dependent queues
Mathematics of Operations Research
Boundary value problems of mathematical physics (vol. 1)
Boundary value problems of mathematical physics (vol. 1)
Asymptotic analysis of the M/G/1 queue with a time-dependent arrival rate
Queueing Systems: Theory and Applications
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Mean characteristics of Markov queueing systems
Automation and Remote Control
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We consider the M(t)/M(t)/m/m queue, where the arrival rate 驴(t) and service rate 驴(t) are arbitrary (smooth) functions of time. Letting pn(t) be the probability that n servers are occupied at time t (0驴 n驴 m, t 0), we study this distribution asymptotically, for m驴驴 with a comparably large arrival rate 驴(t) = O(m) (with 驴(t) = O(1)). We use singular perturbation techniques to solve the forward equation for pn(t) asymptotically. Particular attention is paid to computing the mean number of occupied servers and the blocking probability pm(t). The analysis involves several different space-time ranges, as well as different initial conditions (we assume that at t = 0 exactly n0 servers are occupied, 0驴 n0驴 m). Numerical studies back up the asymptotic analysis.