Adaptive Transmission Strategies and Routing in Mobile Radio Networks

Local throughput in a mobile radio network is roughly defined as the rate at which packets are propagated in specified directions in local network regions. A key factor determining local throughput in an ALOHA or spatial TDMA network with randomly spaced stations is the transmission radius used by the stations. We demonstrate that allowing the transmission radius to depend on the desired direction of propagation can significantly increase local throughput. The local throughput capabilities of a radio network can be effectively used only if adequate routing strategies are employed. This is illustrated by an example based on a symmetric demand assumption for stations uniformly distributed over a disc. I. OPTIMAL FIXED RADIUS SELECTION Suppose that the population of n stations is uniformly distributed within a circle of radius R. If n is large then in small regions the stations are distributed like a Poisson point process with intensity X satisfying n = ~ R ~ x . Assuming that the traffic demand is symmetric (i.e., uniformly distributed over all n(n-1) directed pairs of distinct stations) the mean distance between the source and destination of a packet is (see [ 4 ] , or see [ 2 ] which is a chapter from [ 4 ] ) The network throughput in packet-hops for the ALOHA random access protocol can be approximated by n where A is the area covered by a transmission and A denotes the mean of A . (If the transmission radius is always a constant r then Ais L not random and is euqal to nr2 .) Thus, if denotes the mean forward progress per successful transmission, the network end-to-end throughput in packets per time slot is where Q = L / A . C Since by equation (1.1) the end-to-end throughput is proportional to ?-I we call tl the efficiency of the transmission radius policy. The constant 17 is perhaps more meaningful than y since it does not depend on the network's global geometry and is thus a "local" measure. In [ 4 ] it was assumed that the transmission radius r is the same for all transmissions. The fixed radius r was chosen to maximize the efficiency n over all positive values. It was found that the optimum value of r is such that ?,Ac5.89 that is, the optimum fixed transmission radius is such that the mean number of stations within range of a given station is about six. This choice of transmission radius leads to efficiency 4 -.I351 . 'opt ,fixed r = Using (1.1), this leads to the optimal network throughput .0976 & reported in [ 4 ] . We are quick to remark that much of this analysis is heavily laden with approximations. For example, there is a problem in defining mean forward progress when no station is within range of the transmitter. (We avoid that particular problem in the next section.) See [ 4 ] for further discussion. 11. OPTIMAL ADAPTIVE TRANSMISSION RADIUS Suppose that transmitters can vary their transmission radius with time (rather than using a fixed although optimized radius as in [ 4 ] ) , possibly as a function of the location of the other stations. How might the efficiency be improved? First, we note that once a transmitter has identified an intended receiver for a packet transmission, it should use a transmission radius just large enough to reach that station. It remains to see which of the other stations should be the intended receiver. Suppose a transmitter located at (0,O) must transmit a packet which is ultimately destined for a station with coordinates (z,O) where z is large. If a transmitter at (x,y) is chosen to receive the packet (and to then relay it on) the efficiency for that transmission would be Clearly the adaptive transmission radius rule which maximizes r7 (defined in (1.2)) is to use the radius just large enough to reach the station whose coordinates (x,y) maximize .rl(x,y) over all the stations. This rule is illustrated in Figures 1 and 2. Geometrically, one "scans" the region within a circle centered on the positive x axis which passes through (0,O). The diameter of the circle continuously increases until some station is contained in 'the region. That station becomes the intended receiver and the transmission radius used is the distance to that receiver. We will now compute the efficiency of this rule. All our analysis is under the assumption that n is so large that the distribution of stations located near the fixed station can be assumed to be Poisson with intensity 7, per unit area. Let A be the area of the region which is