Production systems with parallel heterogeneous servers of limited capacity: accurate modeling and performance analysis

Abstract

Heterogeneous systems of limited capacity have general applications in manufacturing, but also for logistic or service systems, due to the differences in server or workstation performance or work assignment, in close relationship with system flexibility, where saturation and blocking are ordinary situations of systems with high demand and limited capacity, so accurate loss quantification is essential for performance evaluation. Multi-class systems of limited capacity have been studied much less than parallel homogeneous systems (Erlang models). In this context, accurate models for parallel heterogeneous ordered-entry systems are developed: without any prior queue, M/Mi/c/c, and with a k capacity queue M/Mi/c/c+k. These new matrix models give an exact state formulation, and their accuracy is verified through discrete event simulation and comparison with literature results. Also, the effect of queue capacity is studied in relationship with the pattern of service rates. Next, the heterogeneous recirculating system model is also developed with good approximation results. Finally, the proposed models are applied to evaluate systems with non-exponential service times, through a new hybrid methodology by combining the Markovian model and the Monte Carlo Method (MCM) for normal or lognormal service times that also yield useful good approximations to the simulated system.