Multivariate probabilistic synthesis of cellular networks teletraffic blocking with poissonian distribution arrival rates

Cellular networks are characterized by mobility in which subscribers move freely within the coverage area. Since the radio spectrum is a scarce resource, the available bandwidth is divided by using a combination of Time- and Frequency-Division Multiple Access (TDMA) Code Division Multiple Access (CDMA) and Frequency Division Multiple Access (FDMA). For communication process to succeed, the subscriber must be allocated some frequency band (FDMA), a time slot (TDMA) or pseudorandom binary sequence that modulates the carrier (CDMA). With the increasing number of users, these resources may become unavailable, leading to new call blocking or handover call blocking. Erlang B and Erlang C have been used in the past to model teletraffic blocking in Public Switched Telephone Network (PSTN). Unfortunately, Erlang B is only ideal when subscribers do not perform call re-attempts after their initial calls are blocked. On the other hand, Erlang C model is applicable only in networks where queuing is applied and can easily lead to higher blocking rates when the number of users is high. This is because it takes into consideration the number of instances in the queue as well as the resources under use. In this paper, teletraffic blocking probabilities that take into account additional cellular network concepts such as the number of mobile stations, call retries, channels reservation, overlays and underlays, user velocity, relative mobility, call priority, call arrival rates and signal to interference plus noise ratio (SINR) were synthesized. The simulation results showed that the developed teletraffic blocking probabilities were superior to the conventional Erlang B and Erlang C as they consider new concepts that exist in cellular networks that were not envisioned in traditional PSTN.