The M/PH/1+D queue with Markov-renewal service interruptions and its application to delayed mobile data offloading

摘要

Motivated by delayed mobile data offloading in cellular networks, we consider an WHO queue with deterministic impatience times (i.e., the M/PI-1/1+D queue), where the server takes ON and OFF states alternately and does not serve any customers in the OFF states. We assume that the state of the server is governed by an alternating Markov renewal process. For this queue, we analyze various performance measures in steady state. Most of the previous studies on the analysis of delayed mobile data offloading assume that service times, ON-and OFF-period lengths, and impatience times are exponentially distributed, and the effect of their distributions on the queueing performance has not been investigated well. We thus discuss the effects of the variability in the service time distribution, the variability in the ON-period distribution, and the correlation between the ON-and OFF-periods, and we show that those factors, especially the variability in service times, has a great impact on the queueing performance. Furthermore, to demonstrate the modeling capability of Markov-renewal service interruptions, we illustrate such models as the mobility of smartphone users in a two-dimensional area is incorporated, and we show how the queueing performance is affected by the geographical distribution of Wi-Fi access points. (C) 2019 Elsevier B.V. All rights reserved.