Blocking probabilities in mobile communications networks with time-varying rates and redialing subscribers

Call-blocking probabilities are among the key performance measures in mobile communications networks. For the analysis of these blocking probabilities, mobile networks can be modelled as networks of Erlang loss queues with common capacity restrictions dictated by the distribution of frequencies over the cells of the network. However, due to the time-varying load offered to the cells of such networks, and due to the mobility pattern of users that varies over time, blocking probabilities usually cannot be obtained in closed form. The relation between networks of Erlang loss queues and networks of infinite server queues, for which also the time-dependent occupancy distribution is known and is given by a multidimensional Poisson distribution, suggests to use that distribution as approximate distribution for the occupancy distribution for the network of Erlang loss queues. This paper extends this so called Modified Offered Load (MOL) approximation to networks of Erlang loss queues with the additional feature that subscribers that find their call blocked attempt to redial to continue their call. For GSM networks operating under Fixed Channel Allocation such that capacity cannot be shared among the cells, it is shown that blocking probabilities are increasing in the redial rates so that the MOL approximation that is most accurate for the maximal value for the redial rates turns out to be a fairly accurate approximation of the upper bound for the blocking probabilities of interest. The accuracy is explicitly evaluated in an application of the results towards analysis of blocking probabilities of subscribers travelling in a hot spot along a road through a GSM network.