Monotonicity of throughput in non-Markovian networks. (English) Zbl 0673.60097

Tsoucas, Pantelis; Walrand, Jean

J. Appl. Probab. 26, No. 1, 134-141 (1989).

In this paper, the throughput of a queueing node at time \(t\geq 0\) is defined to be the number of jobs processed by the node by time t and not, as usual, the time average of this quantity. Monotonicity of this throughput is established in some non-Markovian networks by means of pathwise comparisons. In a series of./GI/s/N queues with loss at the first node it is proved that increasing the waiting room and/or the number of servers increases the throughput. Manufacturing type blocking is shown to perform better than communication-type blocking. For a closed network of./GI/s queues it is shown that the throughput increases as the total number of jobs increases.
The technique used for these results does not apply to blocking systems with finite buffers and feedback. Using a stronger coupling argument, throughput monotonicity as a function of buffer size for a series of two./M/1/N queues with loss and feedback from the second to the first node is proved. Exponential distribution of service times is crucially utilized.

Reviewer: J.Tóth

MSC:

60K25	Queueing theory (aspects of probability theory)
60K20	Applications of Markov renewal processes (reliability, queueing networks, etc.)
60K15	Markov renewal processes, semi-Markov processes
90B22	Queues and service in operations research

Keywords:

pathwise comparison; non-Markovian networks; blocking; coupling argument; throughput monotonicity