The statistical behavior of a loop service system is studied. The system consists of a main station, a server and N stations arranged on a loop. Customers arrive at each station according to a random process. The server makes successive tours along the loop bringing customers from the N stations to the main station. Two related measures of the grade of service are considered: the average queue length and the average virtual waiting time at each station.KEY WORDS AND PHRASES: queueing theory, virtual waiting time, queue length, loop service system, star service system CR CATEGORIES: 3.81, 5.5
ABSTR&CT. A communication system consisting of a number of buffered input terminals connected to a computer by a single channel is analyzed. The terminals are polled in sequence and the data is removed from the terminal's buffer. When the buffer has been emptied, the channel, for an interval of randomly determined length, is used for system overhead and/or to transmit data to the terminals. The system then continues with a poll of the next terminal. The stationary distributions of the length of tile waiting line and the queueing delay are calculated for the case of identically distributed input processes. KEY WORDS AND PHRASES: queueing theory, polling, multidrop CRCATEGOR~ES: 5,5,8.1 IntroductionRecently there has been interest in various types of communication structures for data networks. A survey and extended bibliography can be found in [2]. In this paper we study a communication system under polling. It consists of N buffered terminals or input stations, which "generate" the data, and a central station (e.g. a CPU), which collects the data. This system admits different implementations as a loop or ring network (Figure 1 ); as a multidrop network; as a star network. The essential characteristic of the sytem which we shall consider is the manner by which the channel is allocated to the N users. This service policy has been called polling. Our perspective is that of queueing theory; we view the communication system as a service system. The data play the role of the customers, the channel is the server, and the service operation is the transmission of data from the terminals to the central station. Polling is the term applied to the queue discipline: how the server (channel) is made available to the terminals. We shall model the entry of data into this system by random processes. Our object is to explicate the relationship between the load offered to the system, as modeled by these random processes, and the performance of the system. We shall measure performance in terms of queue lengths and queueing delays. Our analysis assumes, for analytical tractability, buffers of infinite capacity. The distribution of queue
This study is devoted to mean waiting-time approximations in a single-server multi-queue model with cyclic service and zero switching times of the server between consecutive queues. Two different service disciplines are considered: exhaustive service and (ordinary cyclic) nonexhaustive service. For both disciplines it is shown how estimates of the mean waiting times at the various queues can be obtained when no explicit information on arrival intensities and service-time distributions is available, while only the utilizations at the queues and the lengths of the busy periods of the system can be measured. In the exhaustive case, a known mean waiting-time approximation is shown to be suitable for our purposes; in the nonexhaustive case, a new approximation has been derived which is simple and yet more accurate than existing approximations. Extensive simulation validates the approximation methods.
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