Analysis of finite-buffer discrete-time batch-service queue with batch-size-dependent service

• Steady state analysis of single-server finite-buffer discrete-time queue.
• Service time distribution of the batches depend on the batch-size under service.
• Joint distributions of interest are obtained at arbitrary slot boundary.
• Several performance measures of interest are obtained and discussed.
• A cost model is constructed to obtain the optimal value of a key system parameter.

Over the last two decades there has been considerable growth in digital communication systems which operate on a slotted system. In several applications, transmission of packets over the network takes place in batches of varying size, and transmission time depends upon the size of the batch. Performance modelling of these systems is usually done using discrete-time queues. In view of this, we consider a single-server queue with finite-buffer in a discrete-time domain where the packets are transmitted in batches (of varying size) according to minimum and maximum threshold limit, usually known as general batch service rule. The transmission time (in number of slots) of these batches depends on the number of packets within the batch under transmission, and is arbitrarily distributed. We obtain, in steady-state, distribution of the number of packets waiting in the queue and in service (those being transmitted in batches). In addition, we also obtain average number of packets waiting in queue, in the system, with the server, rejection probabilities, etc. Finally, computational experiences with a variety of numerical results have been discussed by introducing a cost model which gives optimum value of the lower threshold limit.