We consider polling models in the sense of Takagi (MIT Press, 1986). In our case, the feature of the server is that it may be forced to wait idly for new messages at an empty queue instead of switching to the next station. We propose four different wait-and-see strategies that govern these waiting periods. We assume Poisson arrivals for new messages and allow general service and switchover time distributions. The results are formulas for the mean average queueing delay and characterisations of the cases where the wait-and-see strategies yield a lower delay compared to the exhaustive strategy.
Polling systems have long been the subject of study and are of particular interest in the analysis of high-speed communications networks. There are many options for the scheduling policies that can be used at each polling station (exhaustive, gated, customer limited, etc.). In addition, one can impose an upper bound on the total service time delivered to customers at a station per server visit. In the most common case the upper bound is a constant for each polling station, and the resulting system model is not Markovian even when service times and interarrival times are exponential. In the paper, a comprehensive solution is developed for the major scheduling policies with time limits for each polling station. The approach is based on studying the embedded Markov chain defined at the sequence of epochs when the server arrives at each polling station. The computation of transition probabilities for the embedded chain requires transient analysis of the Markov process describing the system evolution between epochs. Uniformization methods are used to develop efficient algorithms for the transition probabilities and for system performance measures. Example problems are solved using the techniques developed to illustrate the utility of the results. > In this paper, we consider a cyclic polling system in which arrivals are governed by the Markovian arrival process. Each queue is visited according to the exhaustive time-limited service discipline to coincide with IEEE 802.5 and 802.4 standards. Using the decomposition approach, each queue is analyzed as a single server queue with vacation. By exploiting the properties of the discrete time phase distribution we construct the vacation period from the visit period of the other queues in the polling system. Using an iterative procedure we were able to compute the queue length distribution and the average waiting time for polling systems with finite capacity (or infinite capacity) in all queues. Comparison of the mean waiting time with simulation results shows that the proposed models give reasonable results. We analyze an asymmetric cyclic-service system with multiple queues and nonpreemptive, time-limited service. The time limit for a server visit at each queue is exponentially distributed. Customer service times and changeover times have general distributions. Using discrete Fourier transforms, the queue-length and delay distributions are solved. > This thesis presents models for the performance analysis of a recent communication paradigm: mobile ad hoc networking. The objective of mobile ad hoc networking is to provide wireless connectivity between stations in a highly dynamic environment. These dynamics are driven by the mobility of stations and by breakdowns of stations, and may lead to temporary disconnectivity of parts of the network. Applications of this novel paradigm can be found in telecommunication services, but also in manufacturing systems, road-traffic control, animal monitoring and emergency networking. The performance of mobile ad hoc networks in terms of buffer occupancy and delay is quantified in this thesis by employing specific queueing models, viz., time-limited polling models. These polling models capture the uncontrollable characteristic of link availability in mobile ad hoc networks. Particularly, a novel, so-called pure exponential time-limited, service discipline is introduced in the context of polling systems. The highlighted performance characteristics for these polling systems include the stability, the queue lengths and the sojourn times of the customers. Stability conditions prescribe limits on the amount of tra±c that can be sustained by the system, so that the establishment of these conditions is a fundamental keystone in the analysis of polling models. Moreover, both exact and approximate analysis is presented for the queue length and sojourn time in time-limited polling systems with a single server. These exact analytical techniques are extended to multi-server polling systems operating under the pure time-limited service discipline. Such polling systems with multiple servers effectively may reflect large communication networks with multiple simultaneously active links, while the systems with a single server represent performance models for small networks in which a single communication link can be active at a time. In this paper,we consider two-queue polling model with a Timer and a Randomly-Timed Gated(RTG) mechanism.At queue Q1,we employ a Timer T(1):whenever the server polls queue Q1 and finds it empty,it activates a Timer.If a customer arrives before the Timer expires,a busy period starts in accordance with exhaustive service discipline.However,if the Timer is shorter than the interarrival time to queue Q1,the server does not wait any more and switches back to queue Q2.At queue Q2,we operate a RTG mechanism T(2),that is,whenever the server reenters queue Q2,an exponential time T(2) is activated.If the server empties the queue before T(2),it immediately leaves for queue Q1.Otherwise,the server completes all the work accumulated up to time T(2) and leaves.Under the assumption of Poisson arrivals,general service and switchover time distributions,we obtain probability generating function(PGF) of the queue lengths at polling instant and mean cycle length and Laplace Stieltjes transform(LST) of the workload. Polling systems under the Randomly Timed Gated (RTG) regime are studied and analyzed, and various performance measures are derived. The RTG protocol operates as follows: whenever the server enters a station, a Timer is activated. If the server empties the queue before the Timer‘s expiration, it moves on to the next node. Otherwise (i.e., if there is still work in the station when the Timer expires), the server obeys one of the following rules, each leading to a different model: (1) The server completes all the work accumulated up to the Timer‘s expiration and then moves on to the next node. (2) The server completes only the service of the job currently being served, and moves on. (3) The server stops working immediately and moves on. The RTG protocol defines a wide class of time-based control mechanisms: under rule (1) it spans an entire spectrum of regimes lying between the Gated and the Exhaustive, while under rule (2) it spans an entire spectrum between the 1-Limited and the Exhaustive protocols In this paper, we develop a general framework to analyze polling systems with either the autonomous-server or the time-limited service discipline. According to the autonomous-server discipline, the server continues servicing a queue for a certain period of time. According to the time-limited service discipline, the server continues servicing a queue for a certain period of time or until the queue becomes empty, whichever occurs first. 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 systems. 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-lengths 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.