Queueing analysis of a jockeying model

In this paper, we solve a type of shortest queue problem, which is related to multibeam satellite systems. We assume that the packet interarrival times are independently distributed according to an arbitrary distribution function, that the service times are Markovian with possibly different service rates, that each of the servers has its own buffer for packet waiting, and that jockeying among buffers is permitted. Packets always join the shortest buffer(s). Jockeying takes place as soon as the difference between the longest and shortest buffers exceeds a pre-set number (not necessary 1). In this case, the last packet in a longest buffer jockeys instantaneously to the shortest buffer(s). We prove that the equilibrium distribution of packets in the system is modified vector-geometric. Expressions of main performance measures, including the average number of packets in the system, the average packet waiting time in the system and the average number of jockeying, are given. Based on the above solutions, numerical results are computed. By comparing the results for jockeying and non-jockeying models, we show that a significant improvement of the system performance is achieved for the jockeying model.
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