On-line Frequency Reallocation for Call Requests in Linear Wireless Cellular Networks

On-line frequency allocation problem (FAP) for wireless linear cellular networks reusing the frequency of drop calls is studied. In this paper, FAP is investigated on ring networks. The coverage area of highway that surrounds a large mountain is divided into number of regular hexagonal regions called cells. Each of the cells is aligned with exactly two adjacent cells, thus forming a ring topology of the network. Base station (BS) which heads a cell is the transceiver of new or drop call requests from users of same or neighbouring cells. Utilization of spectrum must be properly managed so that no calls generated from same or adjacent cells should be left without getting services from the BSs. In the proposed on-line algorithm for FAP, the drop call releases frequency, and it is reallocated to an ongoing call using greedy strategy. The algorithm is also implemented on 2- or 3-colourable graph model of ring depending on even or odd number of cells that constitute the network, respectively. The performance of the algorithm is analysed on 2-colourable ring network, and it is found that the competitive ratio of the algorithm is chi/2, where the chromatic number of ring network is chi. It has been also shown that there is no on-line algorithm of less than 1 and 3/2-competitive ratios for FAP in 2-colourable and 3-colourable ring networks, respectively.