ABSTRACT
We have studied several Markov chain models of queuing systems to represent and analyze computer network performance problems. In these models, packets have been assumed to appear instantaneously. The departure time instant of a packet from a queue is considered to be the time instant when the entire packet including the last bit has just completed leaving the system. In the case of the simplest M/M/1/∞ queue in equilibrium, departure time instants are shown to be Poisson. In reality, data packets begin to flow out of the system when the first bit is serviced and continues to flow out for a nonzero amount of time until the last bit has departed. This is easily visualized in the case of a transmitter whose purpose is to move the packet from the system to the surroundings. If we have a sequence of queues, such as the output of the transmitter being fed to a remote receiver, the data packets arriving into the receiver also take a nonzero amount of time for arrival. That is, a packet starts arriving when the first bit starts arriving and continues until the last bit has completed arriving. As mentioned above, if we mark the end of the arrival time interval as the time instant of the packet arrival, the arrival time instants have been shown to be a Poisson stream, if the arrivals came from the departures of a previous M/M/1/∞ queue under equilibrium.
