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Dominance relations in polling systems

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Abstract

In this paper we compare several service disciplines commonly used in polling systems. We present a sample path comparison which allows us to evaluate the efficiency of the different policies based on thetotal amount of work found in the systemat any time. The analysis is carried out for a large variety of polling schemes under fairly general conditions and can be used to construct a hierarchy of the different service schemes.

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Abbreviations

A l :

arrival epoch of thelth customer.

A n(t):

number of type-n customers arriving to the system by timet.

A n(t 1,t 2):

number of customers arriving at queuen during (t 1,t 2).

B 1 :

service time of thelth customer.

Q l :

queue that thelth customer joins.

I(i):

index of the visited queue in theith visit.

S i :

switch-over period succeeding theith visit.

f, g :

service policies.

τ i f :

epoch at which theith service period starts under policyf.

f i (x):

number of customers served in theith service period whenx customers are present in the visited queue when it is polled.

t i f :

epoch at which theith service period ends under policyf.

L n f (t):

number of type-n customers already served by timet under policyf.

C n f (t):

number of type-n customers in the system at timet under policyf.

I f(t):

total amount of time the server was idle during (0,t) under policyf.

U f(t):

total amount of unfinished work at timet in the system under policyf.

C n f (τ i f ,t):

number of candidates at timet (τ i f ≤t≤t i f ) at queuei.

References

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Authors and Affiliations

  1. Computer Science Department, The Raymond Beverly Sackler Faculty of Exact Science, Tel-Aviv University, 69978, Tel-Aviv, Israel

    Hanoch Levy

  2. Electrical Engineering Department, Technion, Israel Institute of Technology, 32000, Haifa, Israel

    Moshe Sidi

  3. Centre for Mathematics and Computer Science, P.O. Box 4079, 1009 AB, Amsterdam, The Netherlands

    Onno J. Boxma

Authors
  1. Hanoch Levy
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  2. Moshe Sidi
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  3. Onno J. Boxma
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Levy, H., Sidi, M. & Boxma, O.J. Dominance relations in polling systems. Queueing Syst 6, 155–171 (1990). https://doi.org/10.1007/BF02411471

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  • DOI: https://doi.org/10.1007/BF02411471

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