Channel Assignment for Time-Varying Demand Sa Liu, Karen Daniels and Kavitha Chandra Center for Advanced Computation and Telecommunications University of Massachusetts Lowell Lowell, MA. 01854 Abstract — This paper presents an integer programming model for dynamic channel assignment (DCA) under space and time-varying traffic demand. The algorithm minimizes the number of channels required to satisfy the traffic de- mand using a threshold based decision criterion on the carrier-to-interference ratio. A neighborhood based search procedure uses the most recent channel state information to perform a feasible assignment when the demand changes. This technique accelerates the convergence of the algorithm to a local minimum and allowsan evaluation of channel gains obtained with increasing neighborhood sizes. This proce- dure will also minimize the number of channel reassignments in cells whose demand is time-invariant. The performanceof a greedy sequential channel assignment heuristic(SA) is ex- amined relative to the spatial distribution of the cells with time-varying demand. Channel gains obtained with DCA relative to the SA scheme range from 30 - 40% for the exam- ples discussed. I. INTRODUCTION Wireless cellular networks are bandwidth and power lim- ited. A finite frequency spectrum is available for provi- sion of commercial services. Based on the service require- ments, the allocated spectrum is divided into a number of channels. Channels are assigned to geographical regions based on expected traffic demand. The reuse of frequen- cies at distances large enough to minimize co-channel in- terference is a basic design principle in cellular networks. Most existing networks have a fixed number of channels assigned (FCA) permanently to each cell for its exclusive use. This arrangement is inefficient for wireless transmis- sion of packet voice, video and data services. The traffic patterns that characterize packet data and video have been found to exhibit high temporal variability [1], [2]. In par- ticular, such packet traffic exhibits persistence in both un- derload and overload conditions for durations longer than that predicted by classical negative exponential distribu- tions. This state-of-affairs will lead to both under utiliza- tion of resources and higher blocking with FCA schemes for bursty traffic sources. The requirement of larger channel bandwidths for broadband transmission will also impose a stronger requirement on optimal allocation of channel re- sources. Dynamic channel assignment (DCA) schemes that can perform at the time-scale of traffic variation are there- S.L. and K.D. are with the Dept. of Computer Science. K.C.iswiththeDept. ofElectricalandComputerEngineeringand was supported in part by NSF under grant ANI-9734585. fore an important component in future wireless networks. Channel assignment schemes that minimize the overhead involved in reassignment of existing calls, while maximiz- ing channel utilization are of particular interest. A survey of fixed, dynamic and hybrid channel assign- ment schemes is provided by Katzela and Naghshineh [3]. The simplest modifications to FCA are based on borrowing channels from the richest neighboring cells to minimize fu- ture call blocking probability. Anderson [4] discusses simu- lation studies of these algorithms and shows that the num- ber of search steps required can limit the performance of the approach. Modifications to reduce the number of search steps have also been considered [5]. This involves channel ordering schemes where the fixed-to-borrowablechannel ra- tio is dynamically varied according to changing traffic con- ditions. In DCA there is no fixed relationship between channels and cells and all channels are available for assignment to all cells. Channel assignment takes place through mini- mization of a cost function such as the allocated band- width under the constraint that channel reuse takes place above specified interference levels. Many instances of this problem are computationally difficult. Murphey et al. [6] provide a comprehensive survey of algorithmic approaches to the problem. Techniques may be broadly classified as graph theoretic, mathematical programming approaches and meta-heuristic search, or some combination thereof. In a typical graph-theoretic abstraction each transmitter is represented by a graph node and two transmitters share a graph edge if using the same channel could create interfer- ence. Graph coloring and Integer programming(IP) formu- lations have been used here [7]. IP formulations also exist for some non-graph-theoretic abstractions. Meta-heuristics of various types have also been employed. Capone and Trubian [8] use a tabu search meta-heuristic that lever- ages search history data to avoid unproductive parts of the search space. Smith and Palaniswami[9] use a combination of neural-networks, simulated annealing and steepest de- scent heuristics to solve a nonlinear IP formulation of the problem. Although a variety of algorithmic models and solution techniques have been proposed for DCA, the performance of such algorithms in the context of varying traffic demand has been examined to a lesser extent. Argyropoulos et al.