Waiting Lines and Times in a System with Polling

Abstract

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

Cyclic reservation schemes for efficient operation of multiple-queue single-server systems

“…The analysis of polling systems with gatcd or exhaustive service has been presentcd in numcrous papers in the literature, e.g.Cooper [11], Eisenberg [13], Konheim and Meister [16] -to mention a few, summarized in a book by Takagi [22], and further surveyed reccntly by Levy and Sidi [17] and Takagi 123).This paper focuses on the study ofschemcs which (1) possess mechanisms for prioritizing the queues, and (2) lcnd themsclves to effective analysis. The combination of these two properties allows designers to affect the system performance as well as to predict the outcome of thcir design.…”

“…Specifically, we focus on two schemes: (1) the Cyclic-Reservation MultipleAcccss (CRMA), which has been proposed by Nassehi t20l for the operation of high-speed local area networks, and (2) the Globally-Gated (GG) scheme, which is a new procedure introduced in this paper and resembles the cyclically Gated [15], in which dynamic rules for optimal operation of two-queue systems are studied; Browne and Yechiali [8,9], in which semi-dynamic rules for minimizing the cycle time are presented; and Boxma et al 16 Els-@eCp-,ncnl= T -1-…”

Deriving Variable Polling Frequency Policies for Pro-active Management in Networks and Distributed Systems

“…Even in the command approach the polling frequency must continuously be adapted in order to avoid control messages as responses. Several existing approaches propose a statistical computation of the polling interval according to the network traffic (Schwartz 1977), buffer occupancy (Konheim and Meister 1974), or particular parameters of network topologies (Ahuja 1982). This computation is rather static because mainly the average values are considered.…”

“…The polling interval is not updated with respect to the behaviour of the polled component. Konheim's and Meister's (1974) statistics model is buffer occupancy-based. Computing formulas focus on the communication invariants at each component (packet-arrival rate, frame-length, average of the walk time).…”

Mean value analysis for polling systems

“…Firstly, each of the approaches can be readily adapted to a discrete-time counterpart, apart from some occasional subtleties (see, e.g., [10,18,21]). The second important observation is that when comparing the use of the aforementioned approaches in the open literature over the recent years, it immediately strikes the eye that the buffer occupancy method and its variations can be -or at least have been -applied to the widest variety of polling systems.…”