Congestion in a loss system when some calls want several devices simultaneously

The problem consists in finding the loss probability of a group of devices to which several categories of traffic are offered, each category occupying a different number of devices. The theory is based on the assumption that the rule for seizing the devices takes into account their total number in the group, and only the present number of active sources. Mathematical derivation assumes a Markov process with a unique stationary state. The case of two categories of traffic, one occupying one device and the other two devices, is considered as an example. It is found that savings in the required number of devices can be achieved when a single group handles both categories. Results of numerical computation of losses in function of the number of devices, for various traffic offered, are shown in graphs. The theory was developed for calculations of the size of a central memory in semielectronic telephone exchanges.