Abstract
We consider a generalization of the classical Erlang loss model with both retrials of blocked calls and a time‐dependent arrival rate. We make exponential‐distribution assumptions so that the number of calls in progress and the number of calls in retry mode form a nonstationary, two‐dimensional, continuous‐time Markov chain. We then approximate the behavior of this Markov chain by two coupled nonstationary, one‐dimensional Markov chains, which we solve numerically. We also develop an efficient method for simulating the two‐dimensional Markov chain based on performing many replications within a single run. Finally, we evaluate the approximation by comparing it to the simulation. Numerical experience indicates that the approximation does very well in predicting the time‐dependent mean number of calls in progress and the times of peak blocking. The approximation of the time‐dependent blocking probability also is sufficiently accurate to predict the number of lines needed to satisfy blocking probability requirements.
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Grier, N., Massey, W.A., McKoy, T. et al. The time‐dependent Erlang loss model with retrials. Telecommunication Systems 7, 253–265 (1997). https://doi.org/10.1023/A:1019176413237
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DOI: https://doi.org/10.1023/A:1019176413237