Exact solution for the initialization time of packet radio networks with two station buffers

The Packet Radio Network (PRNET), a store-and-forward packet-switching system sharing a single radio channel via multi-access techniques and spread spectrum, is an effective communication medium for data and voice transmission in situations requiring fast deployment, non-fixed hardware locations, encryption and anti-jamming in hostile military environments.1-5.14.15 Many investigators have developed analytical solutions for the performance of channel access schemes typically employed (pure ALOHA, ALOHA, CSMA, etc.).1-13 These studies have shown, among other things, that PRNET's can be easily saturated and become unstable unless efficient routing and flow control algorithms are used. To enable point-to-point packet transportation the network station assigns a code (label) to each repeater; the process of assigning such labels is referred to as "network initialization." The initialization procedure assumes that the network topology is not known a priori and is changing with time. Thus, the initialization procedure involves mapping of network topology, determining network structure (labels for repeaters) and transmitting labels to the repeaters. Notwithstanding its importance,t9 the problem of initialization has not been studied extensively except in References 5, 16, 17 and 18. In this paper we present a Markov chain model which enables one to obtain in closed form the optimal rates at which repeaters and station must transmit initialization packets and labels to minimize the network initialization time in a one-hop network, two buffer station. This is an extension of the work reported in References 17 and 18. In Reference 17 a Markov Chain model for initialization of I-hop packet radio networks was discussed; with this model the total initialization time must be obtained numerically by solving a set of linear simultaneous equations. For an m repeater network the number of such equations turns out to be O(m 3 ). Hence, this model is not applicable for analyzing large networks. The complexity of such models can be reduced by modifying the label queue management from a random selection discipline to a first-in, first-out (FIFO) discipline; the number of linear simultaneous equations that need to be solved