Congestion Probabilities in Erlang-Engset Multirate Loss Models under the Multiple Fractional Channel Reservation Policy

Ioannis Moscholios


A communication link that accommodates different service-classes whose
calls have different bandwidth requirements and compete for the available link bandwidth under the Multiple Fractional Channel Reservation (MFCR) policy is considered. The MFCR policy allows the reservation of real (not integer) number of channels in order to benefit calls of high channel (bandwidth) requirements. Two call arrival processes are studied: i) the Poisson (random) process and ii) the quasi-random process. In the first case, calls come from an infinite number of sources, while in the second case calls come from a finite number of sources. To determine call blocking probabilities for Poisson arriving calls, approximate but recursive formulas are proposed based on the notion of reverse transition rates. To determine time and call congestion probabilities for quasi-random arriving calls, approximate but recursive formulas are proved based on the fact that the proposed model does not have a product form solution for the steady state probabilities. The accuracy of the new formulas is verified through simulation and found to be highly satisfactory.


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