Abstract. In this paper, we will develop a general framework to analyze polling systems with either the autonomous-server or the time-limited service discipline. We consider Poisson batch arrivals and phase-type service times. It is known that these disciplines do not satisfy the well-known branching property in polling system. Therefore, hardly any exact results exist in the literature. Our strategy is to apply an iterative scheme that is based on relating in closed-form the joint queue-length at the beginning and the end of a server visit to a queue. These kernel relations are derived using the theory of absorbing Markov chains.
This paper considers polling systems with an autonomous server that remains at a queue for an exponential amount of time before moving to a next queue incurring a generally distributed switch-over time. The server remains at a queue until the exponential visit time expires, also when the queue becomes empty. If the queue is not empty when the visit time expires, service is preempted upon server departure, and repeated when the server returns to the queue. The paper first presents a necessary and sufficient condition for stability, and subsequently analyzes the joint queue-length distribution via an embedded Markov chain approach. As the autonomous exponential visit times may seem to result in a system that closely resembles a system of independent queues, we explicitly investigate the approximation of our system via a system of independent vacation queues. This approximation is accurate for short visit times only.
Ad hoc network routing protocols may fail to operate in the absence of an end-to-end connection from source to destination. This deficiency can be resolved by so-called opportunistic networking which exploits the mobility of the nodes by letting them operate as relays according to the storecarry-and-forward paradigm. However, the efficiency of this approach will depend to a large extent on the contact and inter-contact times of node pairs. In this work, we analyze the delay performance of a small opportunistic network by considering a tandem queueing system. We present an exact packet-level analysis by applying ideas from the polling literature. Due to the state-space expansion, this analysis cannot efficiently be applied for all model parameter settings. For this reason, an analytical approximation is constructed and its excellent performance has extensively been validated. Numerical results on the mean end-to-end delay show that the inter-contact time distribution impacts this metric only through its first two moments. Finally, we study delay optimization under power control.
We develop a queueing model characterizing explicitly the impact of interference on end-to-end performance measures such as throughput in ad hoc networks, emphasizing the performance trade-off between single-path and multi-path routing. It may seem attractive to employ multi-path routing, but as all nodes share a single channel, efficiency may drop due to increased interference levels thus yielding single-path performance for some topologies. We formulate a nonlinear programming problem to optimize network performance. Next, we focus on network capacity and show that for this objective the optimum could be found by solving an exponential number of linear programmes. We propose a greedy algorithm that efficiently searches these programmes to approximate the optimal solution. Numerical results for small topologies provide structural insight in optimal path selection and demonstrate the excellent performance of the proposed algorithm. Besides, larger networks and more advanced scenarios with multiple source-destination pairs and different radio ranges are analyzed.
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