분기/접합 유한용량 폐쇄대기행렬망 일차모멘트 성능에 대한 이론적 고찰

Some First-order Performance Properties in the Closed Fork/Join Queueing Networks with Finite Buffers

In this study, we deal with closed fork/join queueing network with finite buffers and investigate the effects of changing network parameters on throughputs. Introducing the sample path technique, we first show that the departure times of customers at each server are also stochastic ordered, and hence the speeding up services improve the throughputs, and moreover we reveal that the throughput is monotone increasing with respect to buffer capacities regardless of service time distributions. Next, two throughput properties are also presented: the one is the symmetry property with respect to the number of customers and the other is the monotonicity with respect to the joint of buffer size and the number of customers. These properties will be useful in devising efficient algorithms for optimal designing problems.