Blocking Probabilities in Erlang Loss Queues with Advance Reservation

Vrugt, Maartje van de; Litvak, Nelly; Boucherie, Richard J.

doi:10.1080/15326349.2014.900388

Cited by 4 publications

(5 citation statements)

References 11 publications

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“…For large d, the blocking probabilities for both the nonreserving and reserving customers become constant with respect to d. Furthermore, there is a degradation of overall system performance when the service times are deterministic, but a slight improvement when service times are exponential. This verifies the observation of [21] that there are circumstances where reservation improves average blocking performance, and circumstances where it does not. For both types of service time distribution, the blocking probabilities for reserving requests are similar for large enough d, and the difference in performance is largely explained by a significantly lower blocking probability for nonreserving requests with exponential service times compared with deterministic service times.…”

Section: Associated With Each Booking Is a Pair Of Random Variables (supporting

confidence: 85%

“…For both types of service time distribution, the blocking probabilities for reserving requests are similar for large enough d, and the difference in performance is largely explained by a significantly lower blocking probability for nonreserving requests with exponential service times compared with deterministic service times. As suggested by the authors of [21], we believe that this can be explained by the fact that there are more frequent requests for a short service that could fit in before an existing reservation in the exponential case than in the deterministic case.…”

Section: Associated With Each Booking Is a Pair Of Random Variables (mentioning

confidence: 83%

“…We adopt a similar infinite-server approximation for the blocking probability in this paper. For a simple system with a single server, van de Vrugt et al [21] made a number of observations. In particular, the authors identified classes of queues where the advanced reservation increases the blocking probabilities and other classes where it decreases them.…”

Section: Introductionmentioning

confidence: 99%

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Queues with advanced reservations: an infinite-server proxy for the bookings diary

Maillardet

Taylor

2016

Adv. Appl. Probab.

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Queues with advanced reservations are endemic in the real world. In such a queue, the 'arrival' process is an incoming stream of customer 'booking requests', rather than actual customers requiring immediate service. We consider a model with a Poisson booking request process with rate λ. Associated with each request is a pair of independent random variables (R i , S i ) constituting a request for service over a period S i , starting at a time R i into the future. Our interest is in the probability that a customer will be rejected due to capacity constraints. We present a simulation of a finite-capacity queue in which we record the proportion of rejected customers, and then move to an analysis of a queue with infinitely-many servers. Obviously no customers are rejected in the latter case. However, the event that the arrival of the extra customer will cause the number of customers in the queue to exceed C at some point during its service can be used as a proxy for the event that the customer would have been rejected in a system with finite capacity C. We start by calculating the transient and stationary distributions for some performance measures for the infinite-server queue. By observing that the stationary measure for the bookings diary (that is, the list of customers currently on hand, together with their start times and service times) is the same as the law for the entire sample path of an infinite server queue with a specified nonhomogenous Poisson input process, which we call the bookings queue, we are able to write down expressions for the abovementioned probability that, at some time during a requested service, the number of customers exceeds C. This measure serves as a bound for the probability that an incoming arrival would be refused admission in a system with C servers and, for a well-dimensioned system, it is to be hoped that it is a good approximation. We test the quality of this approximation by comparing our analytical results for the infinite-server case against simulation results for the finite-server case.

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Section: Associated With Each Booking Is a Pair Of Random Variables (supporting

confidence: 85%

Section: Associated With Each Booking Is a Pair Of Random Variables (mentioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

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Queues with advanced reservations: an infinite-server proxy for the bookings diary

Maillardet

Taylor

2016

Adv. Appl. Probab.

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“…Several studies that analyze online scheduling problems that are similar to the ORP assume that some distributional information on job arrivals and/or durations is available [12][13][14]. Because the focus in these studies is on exploiting the distributional information, we do not review them.…”

Section: Related Literaturementioning

confidence: 99%

The Online Reservation Problem

Goyal

Gupta

2020

Algorithms

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Many sharing-economy platforms operate as follows. Owners list the availability of resources, prices, and contract-length limits. Customers propose contract start times and lengths. The owners decide immediately whether to accept or decline each proposal, even if the contract is for a future date. Accepted proposals generate revenue. Declined proposals are lost. At any decision epoch, the owner has no information regarding future proposals. The owner seeks easy-to-implement algorithms that achieve the best competitive ratio (CR). We first derive a lower bound on the CR of any algorithm. We then analyze CRs of all intuitive “greedy” algorithms. We propose two new algorithms that have significantly better CRs than that of any greedy algorithm for certain parameter-value ranges. The key idea behind these algorithms is that owners may reserve some amount of capacity for late-arriving higher-value proposals in an attempt to improve revenue. Our contribution lies in operationalizing this idea with the help of algorithms that utilize thresholds. Moreover, we show that if non-optimal thresholds are chosen, then those may lead to poor CRs. We provide a rigorous method by which an owner can decide the best approach in their context by analyzing the CRs of greedy algorithms and those proposed by us.

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“…Lu and Radovanovic (2007) study the asymptotic blocking probabilities when the capacity of the system approaches infinity with sub-exponential resource requirements. van de Vrugt et al (2014) characterize the blocking probabilities for a singleserver queue with deterministic short notice (time between arrival and starting service time) as well as discrete notice times. Maillardet and Taylor (2016) bound the blocking probability via calculating the transient and stationary distributions for several performance measures for the infinite-server queue.…”

Section: Relevant Literaturementioning

confidence: 99%

Revenue Management of Reusable Resources with Advanced Reservations

Chen

Levi

Shi

2017

Production and Operations Management

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W e consider a revenue management problem wherein the seller is endowed with a single type resource with a finite capacity and the resource can be repeatedly used to serve customers. There are multiple classes of customers arriving according to a multi-class Poisson process. Each customer, upon arrival, submits a service request that specifies his service start time and end time. Our model allows customer advanced reservation times and services times in each class to be arbitrarily distributed and correlated. Upon arrival of each customer, the seller must instantaneously decide whether to accept this customer's service request. A customer whose request is denied leaves the system. A customer whose request is accepted is allocated with a specific item of the resource at his service start time. The resource unit occupied by a customer becomes available to other customers after serving this customer. The seller aims to design an admission control policy that maximizes her expected long-run average revenue. We propose a policy called the e-perturbation class selection policy (e-CSP), based on the optimal solution in the fluid setting wherein customers are infinitesimal and customer arrival processes are deterministic, under the restriction that the seller can utilize at most (1 À e) of her capacity for any e 2 (0, 1). We prove that the e-CSP is near-optimal. More precisely, we develop an upper bound of the performance loss of the e-CSP relative to the seller's optimal revenue, and show that it converges to zero with a square-root convergence rate in the asymptotic regime wherein the arrival rates and the capacity grow up proportionally and the capacity buffer level e decays to zero.Our main results about the performance of the e-CSP are as follows:1. Finite upper bound. The expected long-run average revenue loss of the e-CSP has a finite upper bound. (This result is formally stated later in Theorem 1.) 2. Asymptotic optimality. In the asymptotic regime wherein the customer arrival rates and the Chen, Levi, and Shi: Revenue Management with Advanced Reservations Production and Operations Management 26(5), pp. 836-859,

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Blocking Probabilities in Erlang Loss Queues with Advance Reservation

Cited by 4 publications

References 11 publications

Queues with advanced reservations: an infinite-server proxy for the bookings diary

Queues with advanced reservations: an infinite-server proxy for the bookings diary

The Online Reservation Problem

Revenue Management of Reusable Resources with Advanced Reservations

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