A Double-ended Queue with Catastrophes and Repairs, and a Jump-diffusion Approximation

Crescenzo, Antonio Di; Giorno, Virginia; Kumar, B. Krishna; Nobile, Amelia Giuseppina

doi:10.1007/s11009-011-9214-2

Cited by 59 publications

(34 citation statements)

References 25 publications

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“…Stochastic motion with stochastic resetting is of considerable interest due to its broad applicability in statistical [1][2][3][4][5][6][7], chemical [8][9][10][11][12], and biological physics [13,14]; and due to its importance in computer science [15,16], computational physics [17,18], population dynamics [19][20][21], queuing theory [22][23][24] and the theory of search and first-passage [25][26][27]. Particularly, in statistical physics, such motion has become a focal point of recent studies owing to the rich non-equilibrium [2][3][4][5][6][28][29][30] and first-passage [31][32][33][34][35][36] phenomena it displays.…”

Section: Introductionmentioning

confidence: 99%

Invariants of motion with stochastic resetting and space-time coupled returns

2019

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Motion under stochastic resetting serves to model a myriad of processes in physics and beyond, but in most cases studied to date resetting to the origin was assumed to take zero time or a time decoupled from the spatial position at the resetting moment. However, in our world, getting from one place to another always takes time and places that are further away take more time to be reached. We thus set off to extend the theory of stochastic resetting such that it would account for this inherent spatio-temporal coupling. We consider a particle that starts at the origin and follows a certain law of stochastic motion until it is interrupted at some random time. The particle then returns to the origin via a prescribed protocol. We study this model and surprisingly discover that the shape of the steady-state distribution which governs the stochastic motion phase does not depend on the return protocol. This shape invariance then gives rise to a simple, and generic, recipe for the computation of the full steady state distribution. Several case studies are analyzed and a class of processes whose steady state is completely invariant with respect to the speed of return is highlighted. For processes in this class we recover the same steady-state obtained for resetting with instantaneous returns-irrespective of whether the actual return speed is high or low. Our work significantly extends previous results on motion with stochastic resetting and is expected to find various applications in statistical, chemical, and biological physics.

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Section: Introductionmentioning

confidence: 99%

Invariants of motion with stochastic resetting and space-time coupled returns

2019

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“…Conolly, Parthasarathy, and Selvaraju [7] studied double-ended queues with an impatient server or customers. Crescenzo, Giorno, Kumar, and Nobile [8] discussed a double-ended queue with catastrophes and repairs and obtained both the transient and steadystate probability distributions. Moreover, the double-ended queue can be applied to many other areas, for example, computer science, perishable inventory system, and organ allocation system.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium and Optimization in a Double-Ended Queueing System with Dynamic Control

Wang

Liu

2019

Journal of Advanced Transportation

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In this paper, we consider a double-ended queueing system which is a passenger-taxi service system. In our model, we also consider the dynamic taxi control policy which means that the manager adjusts the arrival rate of taxis according to the taxi stand congestion. Under three different information levels, we study the equilibrium strategies as well as socially optimal strategies for arriving passengers by a reward-cost structure. Furthermore, we present several numerical experiments to analyze the relationship between the equilibrium and socially optimal strategies and demonstrate the effect of different information levels as well as several parameters on social benefit.

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“…In this context, a reset is more often referred to as a catastrophe, disaster or decimation and can also be seen as an absorbing or "killing" state that triggers, when reached, a restart or "resurrection" of the process [17]. Similar jump processes have been studied for modelling queues where random "failures" clearing the content or occupation of a queue are followed by "repaired phases" in which the queue functions normally [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Large deviations for Markov processes with resetting

2015

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Markov processes restarted or reset at random times to a fixed state or region in space have been actively studied recently in connection with random searches, foraging, and population dynamics. Here we study the large deviations of time-additive functions or observables of Markov processes with resetting. By deriving a renewal formula linking generating functions with and without resetting, we are able to obtain the rate function of such observables, characterizing the likelihood of their fluctuations in the long-time limit. We consider as an illustration the large deviations of the area of the Ornstein-Uhlenbeck process with resetting. Other applications involving diffusions, random walks, and jump processes with resetting or catastrophes are discussed.

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A Double-ended Queue with Catastrophes and Repairs, and a Jump-diffusion Approximation

Cited by 59 publications

References 25 publications

Invariants of motion with stochastic resetting and space-time coupled returns

Invariants of motion with stochastic resetting and space-time coupled returns

Equilibrium and Optimization in a Double-Ended Queueing System with Dynamic Control

Large deviations for Markov processes with resetting

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