Abstract
It is known that a correlation in either the service or interarrival times causes a deterioration in the performance of a queuing system. This study aimed to determine which of the two correlations—in the service times or in the interarrival times—has a stronger influence on the expected queue length, assuming an identical autocorrelation function in both cases. To achieve this goal, a formula for the expected queue length in a system with correlated arrivals was derived first. This new formula, along with a known formula for the expected queue length in a system with correlated service, was used to compare the influence of the two correlations. Various scenarios were studied, such as cases where the common correlation was positive or negative, where the variance of the service or interarrival time was low or high, and where the system load was low or high. Furthermore, both the time-dependent and the steady-state behaviors of the systems were compared. The following two key observations were made. If the impact of other factors on the queue length is minor, then a positive correlation has a worse effect on the queue length when present in service times than in arrival times. On the contrary, a negative correlation has a worse effect on the queue length when present in arrival times than in service times.
Published Version
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