Search

In this article, we consider the stability of two single-server polling models. More specifically, we will state and prove the stability conditions of single-server polling systems operating under the pure and exhaustive exponential time-limited service discipline. These conditions will be proven for the polling system operating under the periodic polling strategy and preemptive service. The stability proof of the pure time-limited discipline is straightforward as stability may be considered for each queue in isolation. The proof for the exhaustive time-limited discipline is more laborious. We follow the line of proof as introduced by Fricker and Ja\"{i}bi for a large class of service disciplines. Unfortunately, the preemptive nature of the exhaustive time-limited discipline excludes it from this class and as a result substantial efforts are required to modify the proof as to allow for preemptive disciplines. Finally, the extension of the proofs to the Markovian polling strategy is discussed.

In the present article, we analyze a class of time-limited polling systems. In particular, we will derive a direct relation for the evolution of the joint queue-length during the course of a server visit. This will be done both for the pure and the exhaustive exponential time-limited discipline for general service time requirements and preemptive service. More specifically, service of individual customers is according to the preemptive-repeat-random strategy, i.e., if a service is interrupted, then at the next server visit a new service time will be drawn from the original service-time distribution. Moreover, we incorporate customer routing in our analysis, such that it may be applied to a large variety of queueing networks with a single server operating under one of the before-mentioned time-limited service disciplines. We study the time-limited disciplines by performing a transient analysis for the queue length at the served queue. The analysis of the pure time-limited discipline builds on several known results for the transient analysis of the M/G/1 queue. Besides, for the analysis of the exhaustive discipline, we will derive several new results for the transient analysis of an M/G/1 during a busy period. The final expressions (both for the exhaustive and pure case) that we obtain for the key relations generalize previous results by incorporating customer routing or by relaxing the exponentiality assumption on the service times. Finally, based on the interpretation of these key relations, we formulate a conjecture for the key relation for any branching-type service discipline operating under an exponential time-limit.

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 store-carry-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.

Polling models are used as an analytical performance tool in several application areas. In these models, the focus often is on controlling the operation of the server as to optimize some performance measure. For several applications, controlling the server is not an issue as the server moves independently in the system. We present the analysis for such a polling model with a so-called autonomous server. In this model, the server remains for an exogenous random time at a queue, which also implies that service is preemptive. Moreover, in contrast to most of the previous research on polling models, the server does not immediately switch to a next queue when the current queue becomes empty, but rather remains for an exponentially distributed time at a queue. The analysis is based on considering imbedded Markov chains at specific instants. A system of equations for the queue-length distributions at these instant is given and solved for. Besides, we study to which extent the queues in the polling model are independent and identify parameter settings for which this is indeed the case. These results may be used to approximate performance measures for complex multi-queue models by analyzing a simple single-queue model.

Crisis situations require fast regain of control. Wireless ad-hoc networks will enable emergency services to act upon the actual status of the situation by retrieving and exchanging detailed up-to-date information. Deployment of highbandwidth, robust, self-organising ad-hoc networks will therefore enable quicker response to typical hat/where/when questions, than the more vulnerable low-bandwidth communication networks currently in use. This paper addresses a number of results of the projects AAF (Adaptive Ad-hoc Freeband communications) and Easy Wireless that enable high bandwidth robust ad-hoc networking.

Wireless sensor networks are decentralised networks consisting of sensors that can detect events and transmit data to neighbouring sensors. Ideally, this data is eventually gathered in a central base station. Wireless sensor networks have many possible applications. For example, they can be used to detect gas leaks in houses or fires in a forest. In this report, we study data gathering in wireless sensor networks with the objective of minimising the time to send event data to the base station. We focus on sensors with a limited cache and take into account both node and transmission failures. We present two cache strategies and analyse the performance of these strategies for specific networks. For the case without node failures we give the expected arrival time of event data at the base station for both a line and a 2D grid network. For the case with node failures we study the expected arrival time on two-dimensional networks through simulation, as well as the influence of the broadcast range.