Delay analysis of two batch-service queueing models with batch arrivals: Geo(X)/Geo(c)/1

In this paper, we compute the probability generating functions (PGF's) of the customer delay for two batch-service queueing models with batch arrivals. In the first model, the available server starts a new service whenever the system is not empty (without waiting to fill the capacity), while the server waits until he can serve at full capacity in the second model. Moments can then be obtained from these PGF's, through which we study and compare both systems. We pay special attention to the influence of the distribution of the arrival batch sizes. The main observation is that the difference between the two policies depends highly on this distribution. Another conclusion is that the results are considerably different as compared to Bernoulli (single) arrivals, which are frequently considered in the literature. This demonstrates the necessity of modeling the arrivals as batches

Discrete time analysis of a slotted transmission system

This paper concerns the performance analysis of a slotted transmission system. Packets of equal size arrive at the transmission facility which can handle a certain maximum number of packets per time-unit called frame. Transmission is assumed to be gated at the start of frames. Temporary overflow is stored in a buffer with infinite capacity. The packet arrival process is described by a Markov chain with finite state space. We derive the stationary expected number of packets in the buffer and the stationary expected packet delay. We also formulate and describe the implementation of an algorithm to compute these quantities. The accuracy of the algorithm is checked by simulation. A realistic traffic model is given and specific parameters are chosen. Results and numerical aspects are evaluated

Creation and Simulation of a Model for a Discrete Time Buffer System with Interrupted Poisson Arrivals and Uncorrelated Server Interruptions

A mathematical model for a discrete-time buffer system with both arrival and server interruptions is developed. In this model fixed-size packets arrive at the buffer according to a Poisson distribution and are stored there until they can be transmitted over the output channel. Service times are constant and the buffer is assumed to be of infinite size. Both arrival stream as well as the service of the packets are subjected to random interruptions described by Bernoulli processes, where the interruption process of the Poisson input stream is uncorrelated to the interruptions of the output line. Expressions are derived for the mean waiting time, the mean queue length, the average lengths of idle and busy periods of the server, and for the server utilization. The behavior of the system is demonstrated with a computer simulation; the simulation results are used to indicate optimal buffer sizes