Mixed Polling with Rerouting and Applications

Queueing systems with a single server in which customers wait to be served at a finite number of distinct locations (buffers/queues) are called discrete polling systems. Polling systems in which arrivals of users occur anywhere in a continuum are called continuous polling systems. Often one encounters a combination of the two systems: the users can either arrive in a continuum or wait in a finite set (i.e. wait at a finite number of queues). We call these systems mixed polling systems. Also, in some applications, customers are rerouted to a new location (for another service) after their service is completed. In this work, we study mixed polling systems with rerouting. We obtain their steady state performance by discretization using the known pseudo conservation laws of discrete polling systems. Their stationary expected workload is obtained as a limit of the stationary expected workload of a discrete system. The main tools for our analysis are: a) the fixed point analysis of infinite dimensional operators and; b) the convergence of Riemann sums to an integral. We analyze two applications using our results on mixed polling systems and discuss the optimal system design. We consider a local area network, in which a moving ferry facilitates communication (data transfer) using a wireless link. We also consider a distributed waste collection system and derive the optimal collection point. In both examples, the service requests can arrive anywhere in a subset of the two dimensional plane. Namely, some users arrive in a continuous set while others wait for their service in a finite set. The only polling systems that can model these applications are mixed systems with rerouting as introduced in this manuscript.Comment: to appear in Performance Evaluatio

Continuous Polling with Rerouting and Applications to Ferry Assisted Wireless LANs

International audienceIn almost all studied continuous polling systems, the user leaves the system after his service is completed. There are interesting applications, in which the users demand a second service (or more). For example, in a ferry assisted wireless network, for every local data transfer the ferry has to collect the data from the source and then deliver the same to the sink. This type of application can be modeled by polling systems with rerouting. In polling systems with arrivals on a continuum (on a circle), a moving server attends the users as and when it encounters one. When rerouting is supported, after the service is completed, the users can reroute to a different point in the same circle to await another service. We obtain the performance of such a system under quite general conditions, via discretization approach. The results are applied to study a ferry assisted wireless local area network. Our results rely heavily on fixed point analysis of infinite dimensional operators

Analysis and Design of Message Ferry Routes in Sensor Networks using Polling Models

RoutingInternational audienceWe consider a Ferry based Wireless Local Area Network (FWLAN), in which information is forwarded from a base station to sensors, or gathered from sensors to a base station using a moving Ferry. The sensors are scattered in a large area and do not have direct radio connectivity with the base station. The ferry thus serves as a relay that enables communication between the sensors and the base station. Our goal in this paper is to design optimal routes of the Ferry moving along which it distributes/collects the messages. Our analysis and optimization results build heavily on the theory of polling systems which we extend here in order to handle the case of continuous location of the demand. We derive optimal trajectories for various scenarios: uplink, downlink and their combination. We extend some of these results to the case of several base stations and several ferries

Towards a unifying theory on branching-type polling systems in heavy traffic

For a broad class of polling models the evolution of the system at specific embedded polling instants is known to constitute a multi-type branching process (MTBP) with immigration. In this paper we derive heavy-traffic limits for general MTBP-type of polling models. The results generalize and unify many known results on the waiting times in polling systems in heavy traffic, and moreover, lead to new exact results for classical polling models that have not been observed before. To demonstrate the usefulness of the results, we derive closed-form expressions for the LST of the waiting-time distributions for models with cyclic globally-gated polling regimes, and for cyclic polling models with general branching-type service policies. As a by-product, our results lead to a number of asymptotic insensitivity properties, providing new fundamental insights in the behavior of polling models

Towards a unifying theory on branching-type polling models in heavy traffic

htmlabstractFor a broad class of polling models the evolution of the system at specific embedded polling instants is known to constitute a multi-type branching process (MTBP) with immigration. In this paper we derive heavy-traffic limits for general MTBP-type of polling models. The results generalize and unify many known results on the waiting times in polling systems in heavy traffic, and moreover, lead to new exact results for classical polling models that have not been observed before. To demonstrate the usefulness of the results, we derive closed-form expressions for the LST of the waiting-time distributions for models with cyclic globally-gated polling regimes, and for cyclic polling models with general branching-type service policies. As a by-product, our results lead to a number of asymptotic insensitivity properties, providing new fundamental insights in the behavior of polling models

Scheduling algorithms for throughput maximization in time-varying networks with reconfiguration delays

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 247-258).We consider the control of possibly time-varying wireless networks under reconfiguration delays. Reconfiguration delay is the time it takes to switch network resources from one subset of nodes to another and it is a widespread phenomenon observed in many practical systems. Optimal control of networks has been studied to a great extent in the literature, however, the significant effects of reconfiguration delays received limited attention. Moreover, simultaneous presence of time-varying channels and reconfiguration delays has never been considered and we show that it impacts the system fundamentally. We first consider a Delay Tolerant Network model where data messages arriving randomly in time and space are collected by mobile collectors. In this setting reconfiguration delays correspond to travel times of collectors. We utilize a combination of wireless transmission and controlled mobility to improve the system delay scaling with load [rho] from [theta](1/(1-[rho])²) to [theta](1/1-[rho]), where the former is the delay for the corresponding system without wireless transmission. We propose control algorithms that stabilize the system whenever possible and have optimal delay scaling. Next, we consider a general queuing network model under reconfiguration delays and interference constraints which includes wireless, satellite and optical networks as special cases. We characterize the impacts of reconfiguration delays on system stability and delay, and propose scheduling algorithms that persist with service schedules for durations of time based on queue lengths to minimize negative impacts of reconfiguration delays. These algorithms provide throughput-optimality without requiring knowledge of arrival rates since they dynamically adapt inter-switching durations to stochastic arrivals. Finally, we present optimal scheduling under time-varying channels and reconfiguration delays, which is the main contribution of this thesis. We show that under the simultaneous presence of these two phenomenon network stability region shrinks, previously suggested policies are unstable, and new algorithmic approaches are necessary. We propose techniques based on state-action frequencies of Markov Decision Process theory to characterize the network stability region and propose throughput-optimal algorithms. The state-action frequency technique is applicable to a broad class of systems with or without reconfiguration delays, and provides a new framework for characterizing network stability region and developing throughput-optimal scheduling policies.by Güner Dinc̦er C̦elik.Ph.D

Theory of continuous polling systems applied to the Design of Message Ferry Routes in sensor networks

In this paper we focus on a class of polling systems encountered while modeling the ferry based wireless local area network (FWLAN). A moving ferry, while walking in a predetermined cyclic path, communicates with the static nodes (or users) of the network via a wireless link. The ferry is assumed to stop and communicate with a node that has a packet to send or to receive, when it is closest to that node. The location distribution of the node to which or from which a packet arrives is assumed to have a support of positive Lebesgue measure. These features imply that polling models with finite number of queues cannot be used to model the system. We study in this paper the continuous polling systems with service disciplines that model the use of the FWLAN (and that are more complex than the classical exhaustive or gated services). Our approach is based on discretization of the continuous polling model. We propose a special way of discretizing the continuous system such that: 1) the known Pseudo conservation laws can be applied to obtain the stationary expected workload of the discrete systems; 2) the limit, of these ’discretized’ expected workloads, equals the stationary expected workload of the continuous system. Our results rely heavily on fixed point analysis of infinite dimensional operators