The Analysis Of Networks In Manufacturing Systems

Abstract

Suppose customers (products) arrive at a service facility (machine) at times t1, t2, t3, ··· , where tn is the arrival time of the nth customer and wn+tn is the departure time where wn = waiting time which includes service time and queueing time. Suppose there is a network of machines with customers (products) experiencing blocking due to machine breakdowns. Let P(t) be the matrix of transition probabilities among states (machines) of the Markov chain {X(t), t ≥ 0} where X(t) is continuous time stationary and irreducible. Assuming that the Markov chain is strongly mixing, we prove that the times that demand is not met is asymptotically normally distributed.