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Heavy-traffic limits for a many-server queueing network with switchover. (English) Zbl 1282.60091
The authors study a multiclass Markovian queueing network of multi-server stations. Exogenous arrivals in each station follow a non-stationary Poisson process. Each job waiting for the service in a queue may, after some exponentially distributed time depending on the system state, switch to another station or leave the network. The authors study the performance of the network under many-server heavy traffic limiting regimes, including the critically loaded quality-and-efficiency-driven (QED) regime, and the overloaded efficiency-driven (ED) regime. They also study the limits corresponding to the mixture of the under-loaded quality driven (QD) regime with QED and ED regimes. The fluid and diffusion limits of the queue-length processes in all regimes are established in the form of ordinary differential equations and stochastic differential equations, respectively. In the case of the QD regime, the load balancing effect of switchover in the mixed regimes is investigated.

MSC:
60K25 Queueing theory (aspects of probability theory)
60F17 Functional limit theorems; invariance principles
90B22 Queues and service in operations research
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