Approximations for the Repairman Problem with Two Repair Facilities. I. No Spares.
CONTROL ANALYSIS CORP PALO ALTO CALIF
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The model considered here consists of n operating units which are subject to stochastic failure according to an exponential failure time distribution. Failures can be of two types. With probability pq a failure is of type 12 and is sent to repair facility 12 for repair. Repair facility 12 operates as a SSup 1 Sub n SSup 2Sub n-server queue with exponential repair times having parameter Mu sub 1 Mu sub 2. The number of units waiting for or undergoing repair each of the two facilities is a continuous-parameter Markov chain with finite state space. The paper derives limit theorems for the stationary distribution of this Markov chain as n becomes large under the assumption that both S Sup 1 Sub n and SSup 2 Sub n grow linearly with n. These limit theorems give very useful approximations, in terms of the six parameters characterizing the model, to a distribution that would be impossible to use in practice. Author
- Operations Research