On the accuracy of the simple peak hour approximation for Markovian queues

Article Abstract:

A study is conducted to identify the conditions under which accurate estimates are generated by the simple stationary peak hour approximation (SPHA) for measuring peak hour performance in multiserver queueing systems that involve exponential service times and periodic or sinusoidal Poisson arrival processes. Three performance measures are examined: the expected number of customers waiting in queue, the expected time that customers spend waiting for service and the likelihood that a customer is late and will have to wait to be served. These measures are analyzed from the perspectives of long-run average performance, peak hour performance and peak epoch performance. The results indicate that SPHA can be expected to produce very accurate estimates, regardless of the values of other system parameters, when service systems have high service rates, such as telecommunications, banking, information processing and toll booths.

Approximation theory, Approximation

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A network decomposition approach for approximating the steady-state behavior of Markovian multi-echelon reparable item inventory systems

Article Abstract:

A technique is developed for reaching approximate steady-state probabilities for large, multi-echelon inventory systems based as non-Jacksonian Markovian networks with limited state space. The network model is decomposed into smaller, overlapping local subnetwork models, allowing for their solution in isolation, and returning back and forth among the subnetwork models until model convergence is reached. The method is efficient and accurate for this application, according to numerical results.

Probabilistic number theory

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Control variate models for estimating transient performance measures in repairable item systems

Article Abstract:

Infinite source, ample-server models (&/&) can be compared with finite-source, finite-server models (f/f) using a composite control variate method. This use of the (&/&) model as a control variate for (f/f) models is an effective variance reduction technique that can be used to efficiently estimate the performance measures of both types of models. These estimates, in turn, permit the efficient determination of when (&/&) models become good approximations of (f/f) models.

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