A Queueing System Subject to Breakdown and Having Non-stationary Poisson ArrivalsDepartment of Operations Research and Department of Statistics, Stanford University, 1977 - Queuing theory - 23 pages This paper considers a single server queueing system that alternates stochastically between two states: operational and failed. When operational, the system functions as an M/Ek/1 queue. When the system is failed, no service takes place but customers continue to arrive according to a Poisson process; however, the arrival rate is different from that when the system is operational. Thus, both the arrival and service distributions are nonstationary. The durations of the operating and failed periods are exponential with mean 1/c-alpha and Erlang with mean 1/c-beta, respectively. Generating functions are used to derive the steady-state quantities L and W, both of which are decreasing and convex functions of c. The paper includes an analysis of several special and extreme cases and an application to a production-storage system. (Author). |
Common terms and phrases
₁/m³ Andrew W arrive according average number backlogged block number Computation controls how rapidly convex functions customer arrived Data Entered decreasing and convex denotes the number Erlang distribution expected value exponentially distributed expression 27 failed periods G₁(z Go(z H₁(y Ho(y L and W L'Hôpital's rule twice M/E/1 queue mean 1/ca model unless NON-STATIONARY POISSON ARRIVALS NONSTATIONARY POISSON number of phases number of service operational and failed Pi+l,j Poisson arrival process Poisson process production-storage system queue first becomes queue not subject queue with parameters queueing model QUEUEING SYSTEM SUBJECT random variable repair period repair phases remaining REPORT NUMBER Section service and repair service rate shape parameter Shogan special and extreme Stanford University stationary steady-state probabilities subject to breakdown system is failed system is operational system occilates T₂ UNCLASSIFIED SECURITY CLASSIFICATION Yechiali and Naor yields Κμ λ₁