Performance analysis and buffer allocations in some open assembly systems

This paper considers a finite capacity fork–join queueing model for open assembly systems with arrival and departure synchronizations and presents an approach for enumerating the state space and obtaining the steady state probabilities of the same for such a model under exponential assumptions. Several performance measures like the throughput of the system, fraction of arrivals that actually enter into the system, utilizations of the work stations, etc., are obtained. Further, design of such fork–join systems in terms of buffer size configurations for maximizing the throughput of the system, or for minimizing the mean waiting time of a typical job, or for minimizing the Work-In-Process of the system is done using the above performance prediction approach. Such optimal configurations exhibit some interesting features.