On the Optimal Assignment of Servers and Repairman.
CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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Consider an N server queuing system in which service times of server i are exponentially distributed random variables with rate lambda sub i. Customers arrive in accordance with some arbitrary arrival process. If a customer arrives when all servers are busy, then he is lost to the system otherwise, he is assigned to one of the free servers according to some policy. Once a customer is assigned to a server he remains in that status until service is completed. We show that the policy that always assigns an arrival to that free server whose service rate is largest smallest stochastically minimizes maximizes the number in the system. The result is then used to show that in an N component system in which the i superscript th power components up-time is exponential with rate lambda sub i and in which the repair times are exponential with rate mu, the policy of always repairing the failed components whose failure rate lambda is smallest stochastically maximizes the number of working components.
- Numerical Mathematics