ABSTRACT
Consider an unlimited size buffer single server queue with iid exponential service times of rate µ. Interarrival times are iid, but are not necessarily exponential. In the literature, such queues are denoted by GI/M/1/∞. The subscript I emphasizes that the interarrival times are iid. It is not uncommon to drop the subscript I with the understanding that unless otherwise stated, IATs are iid. We will follow this simpler notation. G/M/1 queues appear in applications in which the interarrival times cannot be approximated as memoryless. As an example, packets may arrive periodically and the packet sizes may vary in a way that it can be approximated by an exponential random variable. Erratic arrivals such as with a Pareto IAT and exponential packet sizes also constitutes a G/M/1 queue. This chapter studies the G/M/1/∞ queue. Analysis of finite buffer G/M/1 queue is simple and is briefly treated. The important application example with Pareto interarrival times is included.
