Modified Erlang Loss System for Cognitive Wireless Networks

Evsey Morozov, Stepan Rogozin, Hung Q. Nguyen and Tuan Phung-Duc
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Evsey Morozov: Institute of Applied Mathematical Research, Karelian Research Centre RAS, 185910 Petrozavodsk, Russia
Stepan Rogozin: Institute of Applied Mathematical Research, Karelian Research Centre RAS, 185910 Petrozavodsk, Russia
Hung Q. Nguyen: Graduate School of Science and Technology, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8573, Ibaraki, Japan
Tuan Phung-Duc: Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8573, Ibaraki, Japan

Mathematics, 2022, vol. 10, issue 12, 1-20

Abstract: This paper considers a modified Erlang loss system for cognitive wireless networks and related applications. A primary user has pre-emptive priority over secondary users, and the primary customer is lost if upon arrival all the channels are used by other primary users. Secondary users cognitively use idle channels, and they can stay (either in an infinite buffer or in an orbit) in cases where idle channels are not available upon arrival or they are interrupted by primary users. While the infinite buffer model represents the case with zero sensing time, the infinite orbit model represents the case with positive sensing time. We obtain an explicit stability condition for the cases where arrival processes of primary users and secondary users follow Poisson processes, and their service times follow two distinct arbitrary distributions. The stability condition is insensitive to the service time distributions and implies the maximal throughout of secondary users. Moreover, we extend the stability analysis to the system with outgoing calls. For a special case of exponential service time distributions, we analyze the buffered system in depth to show the effect of parameters on the delay performance and the mean number of interruptions of secondary users. Our simulations for distributions rather than exponential reveal that the mean number of terminations for secondary users is less sensitive to the service time distribution of primary users.

Keywords: cognitive wireless network; regenerative analysis; stability condition; priority queue; Erlang loss system; classical retrials; outgoing calls (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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