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On Little’s Formula in Multiphase Queues

Author

Listed:
  • Saulius Minkevičius

    (Institute of Data Science and Digital Technologies, Vilnius University, Akademijos st. 4,LT-08412 Vilnius, Lithuania)

  • Igor Katin

    (Institute of Data Science and Digital Technologies, Vilnius University, Akademijos st. 4,LT-08412 Vilnius, Lithuania)

  • Joana Katina

    (Institute of Computer Science, Vilnius University, Didlaukio st. 47, LT-08303 Vilnius, Lithuania)

  • Irina Vinogradova-Zinkevič

    (Department of Information Technologies, Vilnius Gediminas Technical University, Saulėtekio al. 11,LT-10223 Vilnius, Lithuania)

Abstract

The structure of this work in the field of queuing theory consists of two stages. The first stage presents Little’s Law in Multiphase Systems (MSs). To obtain this result, the Strong Law of Large Numbers (SLLN)-type theorems for the most important MS probability characteristics (i.e., queue length of jobs and virtual waiting time of a job) are proven. The next stage of the work is to verify the result obtained in the first stage.

Suggested Citation

  • Saulius Minkevičius & Igor Katin & Joana Katina & Irina Vinogradova-Zinkevič, 2021. "On Little’s Formula in Multiphase Queues," Mathematics, MDPI, vol. 9(18), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2282-:d:636899
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    References listed on IDEAS

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    1. Ward Whitt, 1980. "Some Useful Functions for Functional Limit Theorems," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 67-85, February.
    2. Martin I. Reiman, 1984. "Open Queueing Networks in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 9(3), pages 441-458, August.
    3. James R. Jackson, 1963. "Jobshop-Like Queueing Systems," Management Science, INFORMS, vol. 10(1), pages 131-142, October.
    4. Itai Gurvich, 2014. "Validity of Heavy-Traffic Steady-State Approximations in Multiclass Queueing Networks: The Case of Queue-Ratio Disciplines," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 121-162, February.
    5. Siva Theja Maguluri & Sai Kiran Burle & R. Srikant, 2018. "Optimal heavy-traffic queue length scaling in an incompletely saturated switch," Queueing Systems: Theory and Applications, Springer, vol. 88(3), pages 279-309, April.
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    Cited by:

    1. Viacheslav Morozov & Vladimir Shepelev & Viktor Kostyrchenko, 2022. "Modeling the Operation of Signal-Controlled Intersections with Different Lane Occupancy," Mathematics, MDPI, vol. 10(24), pages 1-24, December.

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