Maximum Throughput in Finite-Capacity Open Queueing Networks with Product-Form Solutions

A finite-capacity open queueing network with independent balance is considered. These are systems with customers undergoing stages of service, where the rate of flow into a state due to a customer entering a stage of service is equal to the flow out of that state due to a customer leaving that stage of service. Such systems have the convenient property that the steady-state probability of a given configuration of customers factors into a product of terms, each term involving the configuration at one service center. If service rates are constant for each customer class, and excess arrivals are discarded, then the following two results hold: (1) The maximum possible output rate for the finite-capacity case equals the value of the customer arrival rate which just saturates the slowest server in the infinite-capacity case. (2) An infinite-capacity network can have a strictly greater output rate than the corresponding finite-capacity network, no matter how large the capacity.

• 저널Management Science · 24(2) · 217–223
• 토픽Advanced Queuing Theory Analysis · Management Information Systems
• DOI10.1287/mnsc.24.2.217
• 저자Paul J. Schweitzer