M/G/1 Type Vacation Models: Exhaustive Service

Tian, Naishuo; Zhang, Zhe George

doi:10.1007/978-0-387-33723-4_2

Cited by 7 publications

(13 citation statements)

References 67 publications

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“…A server's server cycle consists of a one or more services followed by one or more vacations. In a loose sense, a vacation can be used to perform maintenance or setup, or do another task (such as serving another queue, for example) [28]. The total duration of service within a service cycle is denoted the service period.…”

Section: A Preliminaries: Vacation and P-limited Vacation Queueingmentioning

confidence: 99%

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Incentive-Vacation Queueing in Extreme Edge Computing: An Analytical Reward-Based Framework

Azmy,

Zorba,

Hassanein

2024

IEEE Open J. Commun. Soc.

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Edge Computing (EC) emerged to address the cloud's shortcomings in meeting demand and latency requirements, leading to a shift in computation closer to the end-user. Extreme Edge Computing (XEC) extends this approach by utilizing nearby user-owned computational resources to support latencysensitive applications in a distributed manner. In this study, we introduce Reward Edge Computing (REC), a variant of XEC, where service providers recruit user devices for infrastructure support, offering rewards in return. We explore the use of Incentive-Vacation Queueing (IVQ) to manage REC and analyze both its long-term and short-term performance. Our analysis focuses on the choice of an Incentive-Vacation Function (IVF), a contractual function between workers and service providers, proposing a tunable model favoring either party. We provide closed-form expressions for long-term worker behavior under uniform workload pricing and analyze the system's overall short-term operation, including the time a worker spends in the system. REC and IVQ aim to commodify computational resources for edge services, akin to sharing economy models like Uber and Airbnb, utilizing user-owned infrastructure.

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Section: A Preliminaries: Vacation and P-limited Vacation Queueingmentioning

confidence: 99%

“…The total duration of service within a service cycle is denoted the service period. Similarly, the total duration of vacations within a service cycle is referred to as the vacation period [27], [28].…”

Section: A Preliminaries: Vacation and P-limited Vacation Queueingmentioning

confidence: 99%

Incentive-Vacation Queueing in Extreme Edge Computing: An Analytical Reward-Based Framework

Azmy,

Zorba,

Hassanein

2024

IEEE Open J. Commun. Soc.

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“…Following Yadin and Naor (1963), various vacation queue models have been studied during the past decades. Interested readers can refer to the comprehensive monograph of Tian and Zhang (2006) and the references therein. In particular, Economou and Kanta (2008) studied an observable queue with server vacations due to breakdowns and developed the equilibrium joining strategy for customers.…”

Section: Strategic Behavior In Vacation Queuesmentioning

confidence: 99%

“…In service systems, allowing servers to take vacations when the congestion level is low can help reduce the system's operating cost and arouse servers' enthusiasm, see Tian and Zhang (2006). An efficient vacation mechanism in practice is to let the server resume service once the system's workload reaches a critical level.…”

Section: Introductionmentioning

confidence: 99%

Pay to activate service in vacation queues

Wang

Liu

Fang

2022

Production and Operations Management

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We study a vacation queueing model where an arriving customer, upon finding the server to be on vacation, is offered an opportunity to pay a fee to instantaneously end the server's vacation, which is referred to as pay‐to‐activate‐service (PTAS). If no one utilizes PTAS, the service will automatically resume when the system's workload reaches a critical level. We investigate customers' equilibrium strategies: (i) joining or balking and (ii) if joining, accepting PTAS or rejecting PTAS, in response to such a mechanism; we show that customers' equilibrium strategies exhibit both avoid‐the‐crowd (ATC) and follow‐the‐crowd (FTC) types of behavior. Our results indicate that the adoption of PTAS is efficient in improving the system performance (e.g., revenue and throughput) when the demand volume is intermediate. We also discover that, upon selecting the appropriate queue‐length information disclosure policy, the service provider has to trade off between collecting a higher revenue through PTAS and improving the system throughput, because revealing the queue‐length information will impact the aforementioned two performance metrics in opposing directions. Finally, we compare our new setting to other common mechanisms including regular vacation queues and pay‐for‐priority queues.

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“…In particular, these are mechanisms like single and multiple vacations, in which the server takes, respectively, exactly one or a number of repeated vacations during which the processing of messages is blocked; T -policy in which the service station is being activated T time units after completing the last busy period; and a threshold-type N -policy in which the server restarts the processing if there are N messages present in the system. In [7], and [31] one can find detailed studies devoted to various types of models with vacation policies.…”

Section: Introductionmentioning

confidence: 99%

Non-stationary departure process in a batch-arrival queue with finite buffer capacity and threshold-type control mechanism

Kempa¹,

Kurzyk²

2022

Kybernetika

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Non-stationary behavior of departure process in a finite-buffer M X /G/1/K-type queueing model with batch arrivals, in which a threshold-type waking up N -policy is implemented, is studied. According to this policy, after each idle time a new busy period is being started with the N th message occurrence, where the threshold value N is fixed. Using the analytical approach based on the idea of an embedded Markov chain, integral equations, continuous total probability law, renewal theory and linear algebra, a compact-form representation for the mixed double transform (probability generating function of the Laplace transform) of the probability distribution of the number of messages completely served up to fixed time t is obtained. The considered queueing system has potential applications in modeling nodes of wireless sensor networks (WSNs) with battery saving mechanism based on threshold-type waking up of the radio. An illustrating simulational and numerical study is attached.

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M/G/1 Type Vacation Models: Exhaustive Service

Cited by 7 publications

References 67 publications

Incentive-Vacation Queueing in Extreme Edge Computing: An Analytical Reward-Based Framework

Incentive-Vacation Queueing in Extreme Edge Computing: An Analytical Reward-Based Framework

Pay to activate service in vacation queues

Non-stationary departure process in a batch-arrival queue with finite buffer capacity and threshold-type control mechanism

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