Eliminating the boundary effect of a large-scale personal communication service network simulation

Reviewer: R. Sambasiva Rao

Personal communications service (PCS) is a wireless communications network [1]. Its area is divided into a number of imaginary cells, each of which is allotted a radio channel. PCS provides communication services for mobile users in a limited geographic region. For each call made by a subscriber, a radiochannel is allotted. Since the total number of voice radiochannels available is limited, phone calls are blocked when all the channels are occupied. In this context, an important aspect of the system design is to achieve a low (less than 1 percent) blocking probability. Simulation is often employed to understand the capacity and performance of PCS networks. Cutting off cells at the edge of the simulated region results in a boundary effect. The simulation models in vogue in the last decade consisted of hexagonal systems with dynamic channel assignment. No doubt, having a large number of cells avoids the boundary effect. The number of cells employed was less than 50, however, due to the limited computer resources. The configuration studied was often a square mesh (S-mesh). Lin and Mak propose wrapping the hexagonal mesh (H-mesh) into a homogeneous graph (all nodes of the graph are topologically identical). This new configuration has the advantage of reduced boundary effect and provides accurate results in hot spot study, even for small networks. In the present simulation study, a dynamic borrowing channel assignment algorithm is used in an object-oriented environment. The purpose of wrapping an H-mesh is to create an infinite H-mesh pattern. The number of phone calls simulated was about 1,000,000. But only data after 10,000 calls were monitored, by which time the transients died out. It has been observed that the call arrivals at the cell form a Poisson process and mean call holding follows an exponential distribution. Assuming that there are 10 channels for every call and each cell has the same traffic, the authors show that the wrapping effect practically disappears (blocking probability is less than 0.001 percent) for a number of cells N>37 . Further studies with an analytical model establish that N=37 is large enough to avoid the wrapping effect. The blocking effect for an S-mesh of similar network size is high (greater than 0.1 percent) and it tends to that of an H-mesh as the network size grows enormously. Hot spot factor ( h ) becomes significant in a model where all the calls in the network have the same offered load ( r ), while the central cell attains a peak load of r ? . It is equal to the product of r and h , when h>1 . This paper demonstrates that wrapped H-mesh simulation requires approximately one-third <__?__Pub Caret>of the number of cells in an S-mesh. Thus it requires less computer time for simulation, but provides results of the same statistical significance.