Performance Evaluation of Space Division Output Buffered Switches

Discrete-time multiserver queues have been successfully used in the performance evaluation of computer and communication systems in various contexts such as TDM, voice-data integration, deflection routing and more recently, ATM-switching technology. In digital communication systems, buffers are used for the temporary storage of digital information awaiting transmission via some communication channel(s). Usually, information presents itself in the form of fixed-size packets, and synchronous (slotted) transmission is used so that the buffers can be modelled as discrete-time queuing systems. In this article, performance analysis of space division output buffered switches operating in an ATM multimedia environment is presented. Fixed size packets arrive onto the switch inputs in each time slot. The switch is modelled as a discrete-time, batch arrival, multiserver queuing system, with infinite buffer and geometric service times. The main contribution of this work is using multiserver case and geometric service time. Many performance measures such as System occupancy, Queuing time, Unfinished work and Waiting time are analysed. Probability Generating Functions (PGFs) and expectations for the corresponding random variables are derived. The results of the analysis have been verified in many ways. First, they have been used to generate the results of some previous analyses as special cases. Second, they obviously seem to preserve classical queuing relations (e.g. the famous Little’s formula). Last, they have been shown to generate intuitively acceptable graphs, when translated into numerical values.