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.
Furthermore, there are several works that investigate polling models with time-limited service. There, messages are served at a station for a certain period of time or until the queue is empty, whichever occurs first. If there is still work at the station when the timer expires, the server either finishes all the present work, or completes only the service of the currently served message, or stops working immediately at this station and switches to the next station. We refer to @cite_11 @cite_3 @cite_12 @cite_6 @cite_13 for random time limits (in particular exponentially distributed timers). @cite_4 and @cite_8 , deterministic time limits are studied.
@cite_4 @cite_8 @cite_6 @cite_3 @cite_13 @cite_12 @cite_11
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We consider two-queue polling models with the special feature that a timer mechanism is employed at Q1: whenever the server polls Q1 and finds it empty, it activates a timer and remains dormant, waiting for the first arrival. If such an arrival occurs before the timer expires, a busy period starts in accordance with Q1's service discipline. However, if the timer is shorter than the interarrival time to Q1, the server does not wait any more and switches back to Q2. We consider three configurations: (i) Q1 is controlled by the 1-limited protocol while Q2 is served exhaustively, (ii) Q1 employs the exhaustive regime while Q2 follows the 1-limited procedure, and (iii) both queues are served exhaustively. In all cases, we assume Poisson arrivals and allow general service and switchover time distributions. Our main results include the queue length distributions at polling instants, the waiting time distributions and the distribution of the total workload in the system. 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 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.