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

Maillardet, Robert; Taylor, Peter G.

doi:10.1017/apr.2015.4

Cited by 4 publications

(2 citation statements)

References 17 publications

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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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Section: Related Literaturementioning

confidence: 99%

The Online Reservation Problem

Goyal

Gupta

2020

Algorithms

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“…() characterize the blocking probabilities for a single‐server queue with deterministic short notice (time between arrival and starting service time) as well as discrete notice times. Maillardet and Taylor () bound the blocking probability via calculating the transient and stationary distributions for several performance measures for the infinite‐server queue. From a technical viewpoint, our work is also related to the stream of literature approximating blocking probabilities for the

M_{t} / G / \infty

queue as well as

M_{t} / G / C / C

loss systems where the arrival process is non‐homogeneous Poisson (e.g., Eick , et al.…”

Section: Introductionmentioning

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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A queue with independent and identically distributed arrivals

Mandjes,

Rutgers

2024

J. Appl. Probab.

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In this paper we consider the workload of a storage system with the unconventional feature that the arrival times, rather than the interarrival times, are independent and identically distributed samples from a given distribution. We start by analyzing the ‘base model’ in which the arrival times are exponentially distributed, leading to a closed-form characterization of the queue’s workload at a given moment in time (i.e. in terms of Laplace–Stieltjes transforms), assuming the initial workload was 0. Then we consider four more general models, each of them having a specific additional feature: (a) the initial workload being allowed to have any arbitrary non-negative value, (b) an additional stream of Poisson arrivals, (c) phase-type arrival times, (d) balking customers. For all four variants the transform of the transient workload is identified in closed form.

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

Cited by 4 publications

References 17 publications

The Online Reservation Problem

The Online Reservation Problem

Revenue Management of Reusable Resources with Advanced Reservations

A queue with independent and identically distributed arrivals

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