Performance limits for channelized cellular telephone systems

Studies the performance of channel assignment algorithms for “channelized” (e.g., FDMA or TDMA) cellular telephone systems, via mathematical models, each of which is characterized by a pair (H,p), where H is a hypergraph describing the channel reuse restrictions, and p is a probability vector describing the variation of traffic intensity from cell to cell. For a given channel assignment algorithm, the authors define T(r) to be the amount of carried traffic, as a function of the offered traffic, where both r and T(r) are measured in Erlangs per channel. They show that for a given H and p, there exists a function TH,p(r), which can be computed by linear programming, such that for every channel assignment algorithm, T(r) ≤ TH,p(r). Moreover, they show that there exist channel assignment algorithms whose performance approaches TH,p (r) arbitrarily closely as the number of channels increases. As a corollary, they show that for a given (H,p) there is a number r0 , which also can be computed by linear programming, such that if the offered traffic exceeds r0, then for any channel assignment algorithm, a positive fraction of all call requests must be blocked, whereas if the offered traffic is less than r0, all call requests can be honored, if the number of channels is sufficiently large. The authors call r0, whose units are Erlangs per channel, the capacity of the cellular system

Channel assignment in cellular radio

Some heuristic channel-assignment algorithms for cellular systems are described. These algorithms have yielded optimal, or near-optimal assignments, in many cases. The channel-assignment problem can be viewed as a generalized graph-coloring problem, and these algorithms have been developed, in part, by suitably adapting some of the ideas previously introduced in heuristic graph-coloring algorithms. The channel-assignment problem is formulated as a minimum-span problem, i.e. a problem wherein the requirement is to find the minimum bandwidth necessary to satisfy a given demand. Examples are presented, and algorithm performance results are discussed

Channel Assignment Algorithms Satisfying Cochannel and Adjacent Channel Reuse Constraints in Cellular Mobile Networks

Improved channel assignment algorithms for cellular networks were designed by modeling the interference constraints in terms of a hypergraph [1]. However, these algorithms only considered cochannel reuse constraints. Receiver filter responses impose restrictions on simultaneous adjacent channel usage in the same cell or in neighboring cells. We first present some heuristics for designing fixed channel assignment algorithms with a minimum number of channels satisfying both cochannel and adjacent channel reuse constraints. An asymptotically tight upper bound for the traffic carried by the system in the presence of arbitrary cochannel and adjacent channel use constraints was developed in [2]. However, this bound is computationally intractable even for small systems like a regular hexagonal cellular system of 19 cells. We have obtained approximations to this bound using the optimal solutions for cochannel reuse constraints only and a further graph theoretic approach. Our approximations are computationally much more efficient and have turned out to track very closely the exact performance bounds in most cases of interest

Fairness in Cellular Mobile Networks

Channel allocation algorithms for channelized cellular systems are discussed from a new perspective, viz., fairness of allocation. The concepts of relative and absolute fairness are introduced and discussed. It will be shown that under certain reasonable assumptions, there exists an absolute (max-min) fair carried traffic intensity vector (a vector describing the traffic carried in the cells of the system). We also show that this vector is unique. We describe some properties of the max-min fair carried traffic intensity vector in an asymptotic limit where the traffic and the number of channels are scaled together. For each traffic pattern, we determine a fixed channel allocation which attains this max-min fair carried traffic intensity vector independent of the value of the offered traffic, in the same asymptotic limit. Finally, we discuss a tradeoff between being max-min fair and trying to maximize revenue. We conclude this correspondence by discussing some possible extensions of our work

Hypergraph Models for Cellular Mobile Communication Systems

Cellular systems have hitherto been modeled mostly by graphs for the purpose of channel assignment. However, hypergraph modeling of cellular systems offers a significant advantage over graph modeling in terms of the total traffic carried by the system. For example, we show that a 37-cell system when modeled by a hypergraph carries around 30% more traffic than when modeled by a graph. We study the performance of channelized cellular systems modeled by hypergraphs in comparison with those modeled by graphs. For this purpose, we have evaluated the capacities of these cellular networks defined [3]. Evaluation of the capacity necessitates generation of maximal independent sets of hypergraphs. We describe some new algorithms that we have developed for this purpose

Performance Limits For Cellular Multiuser Communication Systems

In this paper we will define and study what we call "cellular" multiuser communication systems (MCSs). These systems can be thought of as models for cellular telephone systems using FDMA or TDMA multiaccess protocols

Dynamic channel assignment in cellular radio

Dynamic channel assignment algorithms for cellular systems are developed. The algorithms are compared with an easily simulated bound. Using this bound, it is demonstrated that in the case of homogeneous spatial traffic distribution, some of these algorithms are virtually unbeatable by any channel assignment algorithm. These algorithms are shown to be feasible for implementation in current cellular systems. For the examples considered, in the interesting range of blocking probabilities (2-4%), the dynamic channel assignment algorithms yielded an increase of 60-80% in the carried traffic over the best-known fixed channel assignment

Spectrum efficient frequency assignment for cellular radio

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. In this thesis, we first describe some results on the following generalized chromatic number problem that has its origin in cellular radio (the frequency assignment problem with co-channel constraints only): Given a graph G with vertices V = [...] and an n-vector M = [...] of nonnegative integers (the requirement vector), find the minimum number of colors, [...](G, M), required to assign [...] distinct colors to vertex [...], [...], such that adjacent vertices are assigned disjoint sets of colors. We develop a lower bound on [...](G, M), which generalizes and strengthens the well-known bound [...] n for the usual chromatic number. We show that this bound is sharp for a number of interesting graphs (e.g., perfect graphs and odd cycles), but not for all graphs - the Grotzsch graph being a counterexample. We also give examples of the application of this bound to frequency assignment in cellular radio. In the presence of constraints other than just co-channel constraints (e.g., adjacent channel and co-site constraints), the frequency assignment problem is a further generalization of the graph coloring problem. We describe some heuristic algorithms for frequency assignment in cellular radio that we developed by suitably adapting some of the ideas previously introduced in heuristic graph coloring algorithms. These algorithms have yielded optimal, or near-optimal assignments, in many cases. We then describe some dynamic channel assignment algorithms for cellular systems that we have developed. In addition to having a considerable advantage over fixed channel assignment in the range of blocking probabilities of interest in current cellular systems (2-4%), these algorithms are feasible for implementation in these systems. Some of these dynamic channel assignment algorithms are also shown to give good performance under overload (heavy traffic conditions). Finally, we discuss various methods of computing interference probabilities and the formulation of compatibility constraints on channel assignment based on these calculations. We also formulate the channel assignment problem as one of coloring hypergraphs, instead of graphs, and show that, in the case of dynamic channel assignment, this leads to a considerable increase in the carried traffic for the same blocking probability and the same maximum probability of interference

Optical Networks

831 hlm., 24 c