The pointwise stationary approximation for M(sub.t)/M(sub.t)/s queues is asymptotically correct as the rates increase

Article Abstract:

Researchers have theorized that the pointwise stationary approximation (PSA) is asymptotically correct as rates of service and arrival increase while instantaneous traffic intensity is fixed. L. Green, P. Kolesar, and A. Svoronos used numerical techniques to study how multiserver Markov queues with Poisson arrival processes having sinusoidal arrival rates behave. The researchers developed the PSA, an approximation for long-run average performance measures. The PSA consists of an appropriate weighted average of the measure of performance that occurs at each point in time with a stationary system, with an applicable arrival rate at that point in time. Additional research has confirmed that the research of Green, Kolesar, and Svoronos was correct.

Numerical analysis, Systems theory, Asymptotic distribution (Probability theory), Poisson processes, Green, L., Kolesar, P., Svoronos, A.

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Sensitivity to the service-time distribution in the nonstationary Erlang loss model

Article Abstract:

The stationary Erlang loss model loses its insensitive property when the arrival process is a nonstationary Poisson process. A simple but effective numerical algorithm for the M(sub)t/PH/s/0 is formulated and applied to demonstrate that the service-time distribution beyond the mean can have considerable effects on the time-dependent block probability in the nonstationary Erlang loss model. Aside from this, the results also show that for the case of sinusoidal arrival rates, the peak blocking probability rises as the variability of the service-time distribution is reduced. Findings likewise indicate that steady-state become harder to achieve when there is greater variability in the service-time distribution.

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A light-traffic approximation for single-class departure processes from multi-class queues

Article Abstract:

Research on approximations for single-class departure processes from multi-class queues is described. The emphasis was on light-traffic classes. An approximation is devised and explained in terms of different time scales. The approximation has important implications for parametric decomposition approximation techniques and for data networks.

Operations research, Management science, Analysis, Stochastic analysis

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