An Additional Special Channel, Limited Space Queuing Problem with Service in Batches of Variable Size

This paper studies the transient behavior of a first-come-first-served queuing problem with service in batches of variable size, Poisson input, and exponential service time distribution. Further, when the queue length increases to N, a fixed pre-assigned positive number, a special service channel capable of serving a group of N units and possessing exponential service time distribution is made available and is canceled at the termination of service if the queue length becomes less than N. Also a limited waiting space K is assumed for the waiting line. The Laplace transforms of various probability generating functions are obtained and the corresponding results for the steady state are derived. Finally, some particular cases are discussed.