Light traffic in a cellular system with mobile subscribers and its applications |
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| Institution: | 1. Department of Production and Information Systems, Tokyo Metropolitan Institute of Technology, 6-6 Asahigaoka, Hino-city, Tokyo 191-0065, Japan;2. Alpine, 1-1-8 Nishi-Gotanda, Shinagawa-ku, Tokyo 141-8501, Japan;1. Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA 90089, USA;2. CentraleSupélec, Avenue de la Boulaie, 35576 Cesson-Sévigné, France;3. Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, USA;1. School of Transportation Science and Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150090, PR China;2. School of Traffic and Transportation, Central South University, Changsha, Hunan 410075, PR China;1. Delaware Center for Transportation (DCT), Department of Civil and Environmental Engineering, University of Delaware, Newark, DE 19716, United States;2. Institute for Transportation Research and Education (ITRE), Department of Civil, Construction and Environmental Engineering, North Carolina State University, Centennial Campus, Box 8601, Raleigh, NC 27695-8601, United States;3. School of Sustainable Engineering and the Built Environment, Arizona State University, Tempe, AZ 85281, United States;1. School of Traffic and Transportation Engineering, Central South University, Changsha, Hunan 410075, China;2. School of Computer Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia;3. Research Centre for Integrated Transport Innovation, School of Civil and Environmental Engineering, University of New South Wales, Sydney, NSW 2052, Australia;4. Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China;1. IBM Research – Ireland, Dublin, Ireland;2. Faculty of Computer Science and Mathematics, Universität Passau, Germany |
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| Abstract: | This paper is concerned with a cellular system with mobile subscribers (customers). This system consists of a cell, called the tagged cell, and its adjacent cells. Each cell has some finite number of channels. The sojourn times of customers in the tagged cell have an exponential distribution. Customers in the adjacent cells move to the tagged cell according to a Poisson process whose rate depends on the number of customers in the tagged cell. Each customer without call in progress generates his call according to an exponential distribution and the channel holding times of calls at each cell have a common exponential distribution. We first show that under some restriction, the light traffic limit for the stationary state distribution in the tagged cell is given by a mixture of a Poisson and binominal distributions. Based on the limit, we develop formulae for evaluating the hand-off and blocking probabilities and the mean number of busy channels in the tagged cell. Several numerical examples are presented that demonstrate the practical usefulness of the formulae. |
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