In a communication system, messages are transmitted through M identical channels. Messages are segmented for storage in fixed size buffers (bins). An individual message may require several buffers,...

In a communication system, messages are transmitted through M identical channels. Messages are segmented for storage in fixed size buffers (bins). An individual message may require several buffers, but no buffer contains data from more than one message. When messages release the buffers from which they are transmitted, the buffers are ready for reuse. Assume that messages arrive in a Poisson process with rate ?. The messages are of length L that is exponentially distributed with mean 1/µL. The transmission rate for the messages is R, so that the transmission time is exponential with mean 1/RµL . The messages are stored in buffers. The data field size per buffer is b. Let N be the random variable representing the number of buffers used by a message. (a) Obtain the distribution of N. (b) Obtain the limiting probability that no message is present in the system. (c) Determine the distribution of the number of occupied buffers under statistical equilibrium and its mean and variance in terms of the limiting probability of no messages present in the system. (Pederson and Shah 1972).