TRANSFORM-FREE ANALYSIS OF M G/1/K AND RELATED QUEUES/

Using constructive, sample-path arguments, we derive a variety of tran sform-free results about queue lengths and waiting times for the M/G/1 /K queue. In classical analyses of M/G/1/K, it is typical to work with Markov processes obtained by defining the ''state'' of the system at a time epoch to be the number of customers present and, as supplementa ry information, the remaining service time of the customer, if any, in service. In contrast, the key idea behind our analysis is to work wit h a modified Markov process that has a more-detailed state description . At any time epoch t when the server is busy, we replace ''the number of customers present'' by two variables, namely (a) the number of cus tomers who where (and still are) waiting in the queue immediately afte r the start of the service in progress, and (b) the number of customer s who arrived during that same service but prior to t. We show that th is minor change of state definition, coupled with a rigorous formaliza tion of the intuitive notion of a ''test customer'' (whose viewpoint i s adopted in our analysis of the modified Markov process) makes possib le a surprisingly simple analysis of the M/G/1/K queue. We also show t hat our method can be extended easily to yield similar results for var ious generalizations of the basic M/G/1/K model.