Limiting the oscillations in queues with delayed information through a novel type of delay announcement

Sophia Novitzky (), Jamol Pender (), Richard H. Rand () and Elizabeth Wesson ()
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Sophia Novitzky: Cornell University
Jamol Pender: Cornell University
Richard H. Rand: Cornell University
Elizabeth Wesson: Cornell University

Queueing Systems: Theory and Applications, 2020, vol. 95, issue 3, No 5, 330 pages

Abstract: Abstract Many service systems use technology to notify customers about their expected waiting times or queue lengths via delay announcements. However, in many cases, either the information might be delayed or customers might require time to travel to the queue of their choice, thus causing a lag in information. In this paper, we construct a neutral delay differential equation model for the queue length process and explore the use of velocity information in our delay announcement. Our results illustrate that using velocity information can have either a beneficial or detrimental impact on the system. Thus, it is important to understand how much velocity information a manager should use. In some parameter settings, we show that velocity information can eliminate oscillations created by delays in information. We derive a fixed point equation for determining the optimal amount of velocity information that should be used and find closed-form upper and lower bounds on its value. When the oscillations cannot be eliminated altogether, we identify the amount of velocity information that minimizes the amplitude of the oscillations. However, we also find that using too much velocity information can create oscillations in the queue lengths that would otherwise be stable.

Keywords: Neutral delay-differential equation; Hopf bifurcation; Perturbations method; Operations research; Queueing theory; Fluid limits; Delay announcement; Velocity; 34K40; 34K18; 41A10; 37G15; 34K27 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11134-020-09657-9

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