Bounding moments of sojourn time in M/G/1 FCFS queue with inaccurate job size information and additive error: Some observations from numerical experiments

In this paper consideration is given to the M/G/1 FCFS system in which the service time distribution is not fully known. There is an unknown “theoretical distribution” of the actual service times. But those service times which are known, follow a different distribution, obtained by adding theoretical services times with the error term drawn from a left-truncated normal distribution. The goal is to derive bounds on the response time in the M/G/1 FCFS queue with the unknown “theoretical distribution” that are better than simply using the known service time distribution. In [1] it is shown that in the case when theoretical service times are multiplied by a log-normally distributed error the M/G/1 LCFS queue with resampling gives better upper bounds on the mean response time in the M/G/1 FCFS queue with the “theoretical distribution” of the service times. Here we present some numerical results, which show that once the error becomes additive the result of [1] is not valid any more. In the calculations it was assumed that the unknown “theoretical distribution” is left-truncated Weibull. The new modification of the LCFS resampling policy is suggested, which leads to the lower bounds for the unknown first and second moments of the response time in the M/G/1 FCFS system with the “theoretical distribution” of the service times. Behaviour of mean response times under other service policies is briefly discussed. Copyright © 2018 for the individual papers by the papers’ authors.

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  • 1 Department of Applied Probability and Informatics Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya str., Moscow, 117198, Russian Federation
  • 2 Department of Data Analysis, Decision-Making and Financial Technology Financial University, Government of the Russian Federation, 49 Leningradsky Prospekt, Moscow, 125993, Russian Federation
  • 3 Institute of Informatics Problems of the Federal Research Center “Computer Science and Control, Russian Academy of Sciences, 44-2 Vavilova Str., Moscow, 119333, Russian Federation
Additive error; Additive noise; Inaccurate service time; Left-truncated Weibull distribution; Mean sojourn time; Queueing system; Sojourn time variance
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