Workload and waiting time in a fixed-time loop system

Loop systems arise in many computer, communication, production, and similar stochastic systems. This work focuses on a loop system with Poisson traffic, arbitrary service times, and a non-Markovian fixed-time discipline. Extensive results for this protocol are presented. A workload analysis is performed to quantify queueing times, waiting times, preemption probabilities, and other important measures. A set of lower bounds for the steady-state mean workload is displayed, and from the set of bounds, it is shown that the mean workload obtained from a diffusion approximation is itself a lower bound. Necessary and sufficient conditions for this lower bound to become exact are given, and the maximum error incurred by using the diffusion approximation is also identified. Quantitative relationships between system sojourn time and system workload are established, and it has been found that with exponential service, this relationship depends only on the utilization, even with preemptive service. All results are evaluated by comparing them to simulations and related findings documented in related literature.

[1]  A. Kuczura.  Loss Systems with Mixed Renewal and Poisson Inputs , 1973, Oper. Res..

[2]  Hideaki Takagi,et al.  Stochastic Analysis of Computer and Communication Systems , 1990 .

[3]  Ronald W. Wolff,et al.  Poisson Arrivals See Time Averages , 1982, Oper. Res..

[4]  A. Kuczura,et al.  Queues with mixed renewal and poisson inputs , 1972 .

[5]  B. T. Doshi,et al.  Queueing systems with vacations — A survey , 1986, Queueing Syst. Theory Appl..

[6]  Kin K. Leung.  Cyclic-service systems with nonpreemptive, time-limited service , 1994, IEEE Trans. Commun..

[7]  Bharat T. Doshi.  Conditional and unconditional distributions forM/G/1 type queues with server vacations , 1990, Queueing Syst. Theory Appl..

[8]  G. F. Newell,et al.  Introduction to the Theory of Queues. , 1963 .

[9]  Hideaki Takagi,et al.  Queuing analysis of polling models , 1988, CSUR.

[10]  Raymond G. Vickson,et al.  A simple approximation for mean waiting time in M/G/1 queue with vacations and limited service discipline , 1993, Oper. Res. Lett..

[11]  Stylianos Perrakis,et al.  Moment Inequalities For A Class Of Single Server Queues , 1976 .

[12]  Teunis J. Ott,et al.  On the M/G/1 queue by additional inputs , 1984, Journal of Applied Probability.

[13]  M. J. Fischer,et al.  An Approximation to Queueing Systems with Interruptions , 1977 .

[14]  Klaus Sauer,et al.  Performance Analysis of the Timed Token Protocol of FDDI and FDDI-II , 1991, IEEE J. Sel. Areas Commun..

[15]  Kin K. Leung,et al.  A single-server queue with vacations and gated time-limited service , 1989, IEEE INFOCOM '89, Proceedings of the Eighth Annual Joint Conference of the IEEE Computer and Communications Societies.

[16]  Moshe Sidi,et al.  Polling systems: applications, modeling, and optimization , 1990, IEEE Trans. Commun..

[17]  Kin K. Leung,et al.  Cyclic-Service Systems with Probabilistically-Limited Service , 1991, IEEE J. Sel. Areas Commun..

[18]  Izzet Sahin.  Moment inequalities for a class of stochastic systems , 1978 .

[19]  M. J. Fischer.  Analysis and Design of Loop Service Systems via a Diffusion Approximation , 1977, Oper. Res..

[20]  David Everitt.  A note on the pseudoconservation laws for cyclic service systems with limited service disciplines , 1989, IEEE Trans. Commun..

[21]  Hideaki Takagi.  Effects of the Target Token Rotation Time on the Performance of a Timed-Token Protocol , 1990, Performance.

[22]  U. Narayan Bhat,et al.  A Stochastic System with Scheduled Secondary Inputs , 1971, Oper. Res..