Abstract
AbstractIt is difficult to perform a strict analysis for the GI1GI2/G1G2 single‐device preemptive‐resume priority queue, in which the arrival follows the renewal process and the processing time follows the general distribution. This paper discusses this kind of system and proposes a simple and accurate approximation for the mean queue length which coincides with the strict solution when the arrival is a Poisson process. The proposed approximation is derived by the moment analysis based on the two‐dimensional jump‐diffusion approximation. Furthermore, the diffusion coefficient is corrected based on the Pollaczek‐Khinchin formula for the M/G/1 queue system to improve the accuracy of approximation. The formula is extended to the case of n‐class priority customers. Although the proposed approximation is essentially for the heavy traffic situation, by comparing the result with the strict solutions for GI M/M1M2/1 system and simulations it is shown that the approximation has a sufficient accuracy also for medium and light traffic situations. The result is also compared with other approximations for M GI/G1G2/1 and GI1GI2/G1G2/1 systems, and it is indicated that the proposed approximation has a better accuracy than the past approximations.
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