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

Novitzky, Sophia; Pender, Jamol; Rand, Richard H.; Wesson, Elizabeth

doi:10.1007/s11134-020-09657-9

Cited by 17 publications

(8 citation statements)

References 32 publications

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“…As done similarly in Novitzky et al [22], we can uncouple the delayed part of this system to get the following N equations.…”

Section: Fluid Limitmentioning

confidence: 99%

“…Although there are many application areas for DDEs, our work is motivated by multidelay DDE models from queueing theory. In recent years, there has been a great interest in studying queues with delayed information, see for example [21,24,22,20,8,14,1]. Queues with delayed information is an important area as they describe how information is lagged in information-technology driven systems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multi-Delay Differential Equations: A Taylor Expansion Approach

Doldo¹,

Pender²

2020

Preprint

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It is already well-understood that many delay differential equations with only a single constant delay exhibit a change in stability according to the value of the delay in relation to a critical delay value. Finding a formula for the critical delay is important to understanding the dynamics of delayed systems and is often simple to obtain when the system only has a single constant delay. However, if we consider a system with multiple constant delays, there is no known way to obtain such a formula that determines for what values of the delays a change in stability occurs. In this paper, we present some single-delay approximations to a multi-delay system obtained via a Taylor expansion as well as formulas for their critical delays which are used to approximate where the change in stability occurs in the multi-delay system. We determine when our approximations perform well and we give extra analytical and numerical attention to the two-delay and three-delay settings.

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“…As done similarly in Novitzky et al [22], we can uncouple the delayed part of this system to get the following N equations.…”

Section: Fluid Limitmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multi-Delay Differential Equations: A Taylor Expansion Approach

Doldo¹,

Pender²

2020

Preprint

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“…Several generalizations of the queues-with-choice model have also been studied, including a version with time-varying arrival rates [8] and those that use velocity information in the delay announcement [9]. The queues-with-choice model can also be obtained as a functional law of large numbers' limit of a stochastic queueing process [10].…”

Section: Introductionmentioning

confidence: 99%

Bubbling, Bistable Limit Cycles and Quasi-Periodic Oscillations in Queues with Delayed Information

Collera

2022

Symmetry

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We consider a model describing the length of two queues that incorporates customer choice behavior based on delayed queue length information. The symmetric case, where the values of the time-delay parameter in each queue are the same, was recently studied. It was shown that under some conditions, the stable equilibrium solution becomes unstable as the common time delay passes a threshold value. This one-time stability switch occurs only at a symmetry-breaking Hopf bifurcation where a family of stable asynchronous limit-cycle solutions arise. In this paper, we examine the non-symmetric case, wherein the values of the time-delay parameter in each queue are different. We show that, in contrast to the symmetric case, the non-symmetric case allows bubbling, multiple stability switches and coexistence of distinct families of stable limit cycles. An investigation of the dynamical behavior of the non-symmetric system in a neighborhood of a double-Hopf bifurcation using numerical continuation explains the occurrence of the bistable limit cycles. Quasi-periodic oscillations were also observed due to the presence of torus bifurcations near the double-Hopf bifurcation. These identifications of the underlying mechanisms that cause unwanted oscillations in the system give a better understanding of the effects of providing delayed information and consequently help in better management of queues.

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“…This delay in information can be caused by factors such as the fact that it can take time to process and send information about queue lengths to the customers and thus the information that customers actually receive describes the queue lengths from some amount of time in the past. Queueing systems where customers are provided with delayed information have been studied extensively, see for example Novitzky et al [16], Doldo and Pender [3,2], Doldo et al [6], Novitzky and Pender [13], Novitzky et al [15], Atar and Lipshutz [1], Whitt [23].…”

Section: Introductionmentioning

confidence: 99%

Queues with Delayed Information: Analyzing the Impact of the Choice Model Function

Doldo¹,

Pender²

2022

Preprint

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In this paper, we study queueing systems with delayed information that use a generalization of the multinomial logit choice model as its arrival process. Previous literature assumes that the functional form of the multinomial logit model is exponential. However, in this work we generalize this to different functional forms. In particular, we compute the critical delay and analyze how it depends on the choice of the functional form. We highlight how the functional form of the model can be interpreted as an exponential model where the exponential rate parameter is uncertain. Furthermore, the rate parameter distribution is given by the inverse Laplace-Stieltjes transform of the functional form when it exists. We perform numerous numerical experiments to confirm our theoretical insights.

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

Cited by 17 publications

References 32 publications

Multi-Delay Differential Equations: A Taylor Expansion Approach

Multi-Delay Differential Equations: A Taylor Expansion Approach

Bubbling, Bistable Limit Cycles and Quasi-Periodic Oscillations in Queues with Delayed Information

Queues with Delayed Information: Analyzing the Impact of the Choice Model Function

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