A Simulation Study and Analysis of a Two Station, Waiting Line Network Model
The research is intended to supplement analytical studies of waiting-line network models and simulation studies designed to compare the functioning of such modeled systems under alternative queue disciplines. The model employed consists of two single-channel service stations. The routing of each arriving customer through the two service stations is generated by a stationary Markov chain. The queue discipline is first-come, first-served. The use of the word network to describe such a model is based upon the fact that (at least some) arriving customers require one or more services at more than one service station. This implies that the arrival process at each service station consists of arrivals from outside the system and of departures from other service stations in the network. The two service station model was selected for this initial venture because it possesses the basic network structure without the added involvement caused by system size alone.
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ANALYSIS AND PREDICTION
Theoretical Properties for Sample Parameter Values
IT THE SIMULATION PROGRAM
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analysis analyzed approximation arrival and departure arrival and service arrival process assumptions auto-correlation conditional probability correlation COVO cross-correlation customer n+1 CVJ CVJ departure intervals departure process discussion employed equation equilibrium estimates experimental results experimental run exponential distribution exponential service flow time density H CVJ histograms initial conditions input job flow job routing Job waiting job-shop systems job-shop type k=2 Erlang Laplace transform Markov chain Mean Variance network model number of jobs number of service observed obtained OJ OJ output Poisson-exponential predictive probability density functions problems queue discipline queue lengths queue statistics queueing systems queueing theory RATIO FOR SYSTEM routing transition run lengths selected servers service at service service center arrival service processes service stations simulation run starting condition statistical dependence steady-state mean system departure system parameters system properties SYSTEM STOCHASTIC PROCESSES TABLE tandem systems tape transient behavior utilization ratios VARIANCE RATIO waiting-line network