Performance Analysis of Discrete-Time Queues in Slotted Networks

Many small-scale wireless networks, such as ad hoc networks, operate in a slotted mode with constant packet sizes. The transreceivers have only modest hardware and hence, queuing performance is an important issue. Performance analysis of slotted systems requires more than simply obtaining the performance figures of discrete-time Markov chains. This paper elucidates the importance of characterizing the timing and synchronization details required to correctly formulate the Markov chain and evaluates corresponding performance figures. Two distinct Markov chains are identified in such analysis of any slotted system. The events causing different transitions between the system states are systematically developed for both Markov chains. Relationships between time-averaged performance figures and corresponding expectations in both Markov chains are developed. The approach is demonstrated by providing easier solutions to some slotted systems found in the literature. Key-Words: Discrete-time queues, slotted networks, performance analysis, Markov chains, crossbar switch, timing and synchronization.