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Workload distributions in ASIP queueing networks Queueing Syst. (IF 1.114) Pub Date : 2021-01-02 Onno Boxma, Offer Kella, Uri Yechiali
The workload of a generalized n-site asymmetric simple inclusion process (ASIP) is investigated. Three models are analyzed. The first model is a serial network for which the steady-state Laplace–Stieltjes transform (LST) of the total workload in the first k sites (\(k\le n\)) just after gate openings and at arbitrary epochs is derived. In a special case, the former (just after gate openings) turns
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Deterministic state-based information disclosure policies and social welfare maximization in strategic queueing systems Queueing Syst. (IF 1.114) Pub Date : 2020-12-07 Tesnim Naceur, Yezekael Hayel
Understanding the impact of the queue length information on the behavior of customers is nowadays a hot topic for strategic queueing problems. Particularly, it is important to understand how this information impacts the equilibrium behavior and therefore global performance metrics in order to give some recommendations to service providers for optimizing their objective. Recent works are focused on
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Equilibrium points and equilibrium sets of some $$\textit{GI}/M/1$$ GI / M / 1 queues Queueing Syst. (IF 1.114) Pub Date : 2020-12-05 N. Hemachandra, Kishor Patil, Sandhya Tripathi
Queues can be seen as a service facility where quality of service (QoS) is an important measure for the performance of the system. In many cases, the queue implements the optimal admission control (either discounted or average) policy in the presence of holding/congestion cost and revenue collected from admitted customers. In this paper, users offer an arrival rate at stationarity that depends on the
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Directed FCFS infinite bipartite matching Queueing Syst. (IF 1.114) Pub Date : 2020-12-01 Gideon Weiss
We consider an infinite sequence consisting of agents of several types and goods of several types, with a bipartite compatibility graph between agent and good types. Goods are matched with agents that appear earlier in the sequence using FCFS matching, if such are available, and are lost otherwise. This model may be used for two-sided queueing applications such as ride sharing, Web purchases, organ
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Strategic behavior and optimization in a hybrid M/M/1 queue with retrials Queueing Syst. (IF 1.114) Pub Date : 2020-11-16 Yoav Kerner, Ophir Shmuel-Bittner
In standard queues, when there are waiting customers, service completions are followed by service commencements. In retrial queues, this is not the case. In such systems, customers try to receive service at a time of their choosing, or the server seeks the next customer for a non-negligible time. In this note, we consider a hybrid model with both a finite standard queue and an orbit. While in the orbit
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Extremal GI / GI /1 queues given two moments: exploiting Tchebycheff systems Queueing Syst. (IF 1.114) Pub Date : 2020-11-09 Yan Chen, Ward Whitt
This paper studies tight upper bounds for the mean and higher moments of the steady-state waiting time in the GI/GI/1 queue given the first two moments of the interarrival-time and service-time distributions. We apply the theory of Tchebycheff systems to obtain sufficient conditions for classical two-point distributions to yield the extreme values. These distributions are determined by having one mass
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Asymptotic properties of the occupation measure in a multidimensional skip-free Markov-modulated random walk Queueing Syst. (IF 1.114) Pub Date : 2020-11-03 Toshihisa Ozawa
We consider a discrete-time d-dimensional process \(\{{\varvec{X}}_n\}=\{(X_{1,n},X_{2,n},\ldots ,X_{d,n})\}\) on \({\mathbb {Z}}^d\) with a background process \(\{J_n\}\) on a countable set \(S_0\), where individual processes \(\{X_{i,n}\},i\in \{1,2,\ldots ,d\},\) are skip free. We assume that the joint process \(\{{\varvec{Y}}_n\}=\{({\varvec{X}}_n,J_n)\}\) is Markovian and that the transition probabilities
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Equilibrium in a finite capacity M / M /1 queue with unknown service rates consisting of strategic and non-strategic customers Queueing Syst. (IF 1.114) Pub Date : 2020-10-14 S. Srivatsa Srinivas, Rahul R. Marathe
We consider an \(M/M/1/{\overline{N}}\) observable non-customer-intensive service queueing system with unknown service rates consisting of strategic impatient customers who make balking decisions and non-strategic patient customers who do not make any decision. In the queueing game amongst the impatient customers, we show that there exists at least one pure threshold strategy equilibrium in the presence
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Product forms for FCFS queueing models with arbitrary server-job compatibilities: an overview Queueing Syst. (IF 1.114) Pub Date : 2020-10-14 Kristen Gardner, Rhonda Righter
In recent years, a number of models involving different compatibilities between jobs and servers in queueing systems, or between agents and resources in matching systems, have been studied, and, under Markov assumptions and appropriate stability conditions, the stationary distributions have been shown to have product forms. We survey these results and show how, under an appropriate detailed description
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A survey on skill-based routing with applications to service operations management Queueing Syst. (IF 1.114) Pub Date : 2020-10-04 Jinsheng Chen, Jing Dong, Pengyi Shi
Service systems often feature multiple classes of customers with different service needs and multiple pools of servers with different skillsets. How to efficiently match customers of different classes with servers of different skillsets is of great importance to the management of these systems. In this survey, we review works on skill-based routing in queues. We first summarize key insights on routing/scheduling
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Tail asymptotics for the $$M_1,M_2/G_1,G_2/1$$ M 1 , M 2 / G 1 , G 2 / 1 retrial queue with non-preemptive priority Queueing Syst. (IF 1.114) Pub Date : 2020-09-29 Bin Liu, Yiqiang Q. Zhao
Stochastic networks with complex structures are key modelling tools for many important applications. In this paper, we consider a specific type of network: retrial queueing systems with priority. This type of queueing system is important in various applications, including telecommunication and computer management networks with big data. The system considered here receives two types of customers, of
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Knowledge, congestion, and economics: Parameter uncertainty in Naor’s model Queueing Syst. (IF 1.114) Pub Date : 2020-09-24 Ying Chen, John J. Hasenbein
This paper studies an extension of Naor’s model in which there is parameter uncertainty. In particular, the arrival rate is known, to customers and system managers, only through its distribution. For the observable case, the relationship between the optimal individual threshold and the thresholds for a social optimizer or revenue maximizer does not change from the classical model with a known arrival
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Strategic behaviour in a tandem queue with alternating server Queueing Syst. (IF 1.114) Pub Date : 2020-09-09 Nimrod Dvir, Refael Hassin, Uri Yechiali
This paper considers an unobservable two-site tandem queueing system attended by an alternating server. We study the strategic customer behaviour under two threshold-based operating policies, applied by a profit-maximizing server, while customers’ strategic behaviour and server’s switching costs are taken into account. Under the Exact-N policy, in each cycle the server first completes service of N
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Speed of convergence to the quasi-stationary distribution for Lévy input fluid queues Queueing Syst. (IF 1.114) Pub Date : 2020-08-10 Zbigniew Palmowski, Maria Vlasiou
In this note, we prove that the speed of convergence of the workload of a Lévy-driven queue to the quasi-stationary distribution is of order 1/t. We identify also the Laplace transform of the measure giving this speed and provide some examples.
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Fluid and diffusion models for a system of taxis and customers with delayed matching Queueing Syst. (IF 1.114) Pub Date : 2020-08-10 Lu Wang, Vidyadhar Kulkarni
We study a system of taxis and customers with Poisson arrivals and exponential patience times. We model a delayed matching process between taxis and customers using a matching rate \(\theta \) as follows: if there are i taxis and j customers in the system, the next pairing will occur after an exponential amount of time with rate \(\theta i^{\delta _1}j^{\delta _2}\) (\(\delta _1, \delta _2 \in (0,+\infty
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Analysis of a discrete-time two-class randomly alternating service model with Bernoulli arrivals Queueing Syst. (IF 1.114) Pub Date : 2020-08-01 Arnaud Devos, Joris Walraevens, Dieter Fiems, Herwig Bruneel
We analyze a discrete-time two-class queueing system with a single server which is alternately available for only one customer class. The server is each time allocated to a customer class for a geometrically distributed amount of time. Service times of the customers are deterministically equal to 1 time slot each. During each time slot, both classes can have at most one arrival. The bivariate process
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Matching queues with reneging: a product form solution Queueing Syst. (IF 1.114) Pub Date : 2020-07-10 Francisco Castro, Hamid Nazerzadeh, Chiwei Yan
Motivated by growing applications in two-sided markets, we study a parallel matching queue with reneging. Demand and supply units arrive to the system and are matched in an FCFS manner according to a compatibility graph specified by an N-system. If they cannot be matched upon arrival, they queue and may abandon the system as time goes by. We derive explicit product forms of the steady-state distributions
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Markovian bulk-arrival and bulk-service queues with general state-dependent control Queueing Syst. (IF 1.114) Pub Date : 2020-07-05 Anyue Chen; Xiaohan Wu; Jing Zhang
We study a modified Markovian bulk-arrival and bulk-service queue incorporating general state-dependent control. The stopped bulk-arrival and bulk-service queue is first investigated, and the relationship between this stopped queue and the full queueing model is examined and exploited. Using this relationship, the equilibrium behaviour for the full queueing process is studied and the probability generating
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Maximum on a random time interval of a random walk with infinite mean Queueing Syst. (IF 1.114) Pub Date : 2020-06-23 Denis Denisov
Let \(\xi _1,\xi _2,\ldots \) be independent, identically distributed random variables with infinite mean \({\mathbf {E}}[|\xi _1|]=\infty .\) Consider a random walk \(S_n=\xi _1+\cdots +\xi _n\), a stopping time \(\tau =\min \{n\ge 1: S_n\le 0\}\) and let \(M_\tau =\max _{0\le i\le \tau } S_i\). We study the asymptotics for \({\mathbf {P}}(M_\tau >x),\) as \(x\rightarrow \infty \).
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Limiting the oscillations in queues with delayed information through a novel type of delay announcement Queueing Syst. (IF 1.114) Pub Date : 2020-06-16 Sophia Novitzky; Jamol Pender; Richard H. Rand; Elizabeth Wesson
Many service systems use technology to notify customers about their expected waiting times or queue lengths via delay announcements. However, in many cases, either the information might be delayed or customers might require time to travel to the queue of their choice, thus causing a lag in information. In this paper, we construct a neutral delay differential equation model for the queue length process
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Batch service systems with heterogeneous servers Queueing Syst. (IF 1.114) Pub Date : 2020-06-11 Jan-Kees van Ommeren; Niek Baer; Nishant Mishra; Debjit Roy
Bulk-service multi-server queues with heterogeneous server capacity and thresholds are commonly seen in several situations such as passenger transport or package delivery services. In this paper, we develop a novel decomposition-based solution approach for such queues using arguments from renewal theory. We then obtain the distribution of the waiting time measure for multi-type server systems. We also
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Stability of JSQ in queues with general server-job class compatibilities Queueing Syst. (IF 1.114) Pub Date : 2020-06-03 James Cruise; Matthieu Jonckheere; Seva Shneer
We consider Poisson streams of exponentially distributed jobs arriving at each edge of a hypergraph of queues. Upon arrival, an incoming job is routed to the shortest queue among the corresponding vertices. This generalizes many known models such as power-of-d load balancing and JSQ (join the shortest queue) on generic graphs. We prove that stability in this model is achieved if and only if there exists
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The distribution of age-of-information performance measures for message processing systems Queueing Syst. (IF 1.114) Pub Date : 2020-06-02 George Kesidis; Takis Konstantopoulos; Michael A. Zazanis
The idea behind the recently introduced “age-of-information” performance measure of a network message processing system is that it indicates our knowledge regarding the “freshness” of the most recent piece of information that can be used as a criterion for real-time control. In this foundational paper, we examine two such measures, one that has been extensively studied in the recent literature and
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Stein’s method for diffusive limits of queueing processes Queueing Syst. (IF 1.114) Pub Date : 2020-06-02 Eustache Besançon; Laurent Decreusefond; Pascal Moyal
Donsker’s theorem is perhaps the most famous invariance principle result for Markov processes. It states that, when properly normalized, a random walk behaves asymptotically like a Brownian motion. This approach can be extended to general Markov processes whose driving parameters are taken to a limit, which can lead to insightful results in contexts like large distributed systems or queueing networks
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An alternative approach to heavy-traffic limits for finite-pool queues Queueing Syst. (IF 1.114) Pub Date : 2020-05-16 G. Bet
We consider a model for transitory queues in which only a finite number of customers can join. The queue thus operates over a finite time horizon. In this system, also known as the \(\Delta _{(i)}/G/1\) queue, the customers decide independently when to join the queue by sampling their arrival time from a common distribution. We prove that, when the queue satisfies a certain heavy-traffic condition
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Mobility can drastically improve the heavy traffic performance from $$\frac{1}{1-\varrho }$$11-ϱ to $$\log (1/(1-\varrho ))$$log(1/(1-ϱ)) Queueing Syst. (IF 1.114) Pub Date : 2020-03-23 Florian Simatos; Alain Simonian
We study a model of wireless networks where users move at speed \(\theta \ge 0\), which has the original feature of being defined through a fixed-point equation. Namely, we start from a two-class processor-sharing queue to model one representative cell of this network: class 1 users are patient (non-moving) and class 2 users are impatient (moving). This model has five parameters, and we study the case
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Waiting time and queue length analysis of Markov-modulated fluid priority queues Queueing Syst. (IF 1.114) Pub Date : 2020-03-09 Gábor Horváth
This paper considers a multi-type fluid queue with priority service. The input fluid rates are modulated by a Markov chain, which is common for all fluid types. The service rate of the queue is constant. Various performance measures are derived, including the Laplace–Stieltjes transform and the moments of the stationary waiting time of the fluid drops and the queue length distributions. An Erlangization-based
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Algorithms for the upper bound mean waiting time in the GI / GI /1 queue Queueing Syst. (IF 1.114) Pub Date : 2020-02-29 Yan Chen; Ward Whitt
It has long been conjectured that the tight upper bound for the mean steady-state waiting time in the GI/GI/1 queue given the first two moments of the interarrival-time and service-time distributions is attained asymptotically by two-point distributions. The two-point distribution for the interarrival time has one mass point at 0, but the service-time distribution involves a limit; there is one mass
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Stability conditions for a multiserver queueing system with a regenerative input flow and simultaneous service of a customer by a random number of servers Queueing Syst. (IF 1.114) Pub Date : 2020-02-21 L. G. Afanaseva; S. A. Grishunina
We investigate the stability condition of a multiserver queueing system. Each customer needs simultaneously a random number of servers to complete the service. The times taken by each server are independent. The input flow is assumed to be a regenerative one. The service time has an exponential, phase-type or hyper-exponential distribution. The stability criteria for the models are established. It
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Ticket queues with regular and strategic customers Queueing Syst. (IF 1.114) Pub Date : 2020-02-15 Gabi Hanukov; Shoshana Anily; Uri Yechiali
We study a Markovian single-server ticket queue where, upon arrival, each customer can draw a number from a take-a-number machine, while the number of the customer currently being served is displayed on a panel. The difference between the above two numbers is called the “virtual queue length.” We consider a nonhomogeneous population of customers comprised of two types: “regular” and “strategic.” Upon
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Analysis of the infinite server queues with semi-Markovian multivariate discounted inputs Queueing Syst. (IF 1.114) Pub Date : 2020-02-14 Landy Rabehasaina; Jae-Kyung Woo
We consider a general k-dimensional discounted infinite server queueing process (alternatively, an incurred but not reported claim process) where the multivariate inputs (claims) are given by a k-dimensional finite-state Markov chain and the arrivals follow a renewal process. After deriving a multidimensional integral equation for the moment-generating function jointly to the state of the input at
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On classes of Bitcoin-inspired infinite-server queueing systems Queueing Syst. (IF 1.114) Pub Date : 2020-01-09 Brian Fralix
We analyze the time-dependent behavior of various types of infinite-server queueing systems, where, within each system we consider, jobs interact with one another in ways that induce batch departures from the system. One example of such a queue was introduced in the recent paper of Frolkova and Mandjes (Stochastic Models, 2019) in order to model a type of one-sided communication between two users in
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Stationary distributions and convergence for M / M /1 queues in interactive random environment Queueing Syst. (IF 1.114) Pub Date : 2020-01-08 Guodong Pang; Andrey Sarantsev; Yana Belopolskaya; Yuri Suhov
A Markovian single-server queue is studied in an interactive random environment. The arrival and service rates of the queue depend on the environment, while the transition dynamics of the random environment depend on the queue length. We consider in detail two types of Markov random environments: a pure jump process and a reflected jump diffusion. In both cases, the joint dynamics are constructed so
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Heavy-traffic limits for stationary network flows Queueing Syst. (IF 1.114) Pub Date : 2020-01-07 Ward Whitt; Wei You
This paper studies stationary customer flows in an open queueing network. The flows are the processes counting customers flowing from one queue to another or out of the network. We establish the existence of unique stationary flows in generalized Jackson networks and convergence to the stationary flows as time increases. We establish heavy-traffic limits for the stationary flows, allowing an arbitrary
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Benchmark policies for utility-carrying queues with impatience Queueing Syst. (IF 1.114) Pub Date : 2020-01-02 Yael Deutsch; Israel David
Men and jobs alike are characterized by a single trait, which may take on categorical values according to given population frequencies. Men arrive to the system following a Poisson process and wait till jobs are assigned to them. Jobs arrive to the system following another, independent, Poisson process. An arriving job must be assigned to a waiting man immediately, or be discarded, ensuing no gain
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Stationary distribution convergence of the offered waiting processes for $$GI/GI/1+GI$$GI/GI/1+GI queues in heavy traffic Queueing Syst. (IF 1.114) Pub Date : 2019-12-03 Chihoon Lee; Amy R. Ward; Heng-Qing Ye
A result of Ward and Glynn (Queueing Syst 50(4):371–400, 2005) asserts that the sequence of scaled offered waiting time processes of the \(GI/GI/1+GI\) queue converges weakly to a reflected Ornstein–Uhlenbeck process (ROU) in the positive real line, as the traffic intensity approaches one. As a consequence, the stationary distribution of a ROU process, which is a truncated normal, should approximate
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Analysis of polling models with a self-ruling server Queueing Syst. (IF 1.114) Pub Date : 2019-11-22 Jan-Kees van Ommeren; Ahmad Al Hanbali; Richard J. Boucherie
Polling systems are systems consisting of multiple queues served by a single server. In this paper, we analyze polling systems with a server that is self-ruling, i.e., the server can decide to leave a queue, independent of the queue length and the number of served customers, or stay longer at a queue even if there is no customer waiting in the queue. The server decides during a service whether this
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Queue length asymptotics for the multiple-server queue with heavy-tailed Weibull service times Queueing Syst. (IF 1.114) Pub Date : 2019-11-10 Mihail Bazhba; Jose Blanchet; Chang-Han Rhee; Bert Zwart
We study the occurrence of large queue lengths in the GI / GI / d queue with heavy-tailed Weibull-type service times. Our analysis hinges on a recently developed sample path large-deviations principle for Lévy processes and random walks, following a continuous mapping approach. Also, we identify and solve a key variational problem which provides physical insight into the way a large queue length occurs
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Analysis of the shortest relay queue policy in a cooperative random access network with collisions Queueing Syst. (IF 1.114) Pub Date : 2019-10-25 M. Saxena; I. Dimitriou; S. Kapodistria
The aim of this work concerns the performance analysis of systems with interacting queues under the join the shortest queue policy. The case of two interacting queues results in a two-dimensional random walk with bounded transitions to non-neighboring states, which in turn results in complicated boundary behavior. Although this system violates the conditions of the compensation approach due to the
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Large deviations of bivariate Gaussian extrema Queueing Syst. (IF 1.114) Pub Date : 2019-10-15 Remco van der Hofstad; Harsha Honnappa
We establish sharp tail asymptotics for componentwise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the existence of a restricted large deviations principle and identify the unique rate function associated with these asymptotics. Our results identify when the maxima of
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Stability of a multi-class multi-server retrial queueing system with service times depending on classes and servers Queueing Syst. (IF 1.114) Pub Date : 2019-10-11 Bara Kim; Jeongsim Kim
We consider a multi-class multi-server retrial queueing system. Customers of each class arrive from outside the system according to a Poisson process. The service times for each class of customers are assumed to be exponentially distributed with service rates depending on both the customers’ class and the servers. We define the offered load and provide stability and instability conditions for this
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Stability conditions for a decentralised medium access algorithm: single- and multi-hop networks Queueing Syst. (IF 1.114) Pub Date : 2019-10-11 Seva Shneer; Alexander Stolyar
We consider a decentralised multi-access algorithm, motivated primarily by the control of transmissions in a wireless network. For a finite single-hop network with arbitrary interference constraints, we prove stochastic stability under the natural conditions. For infinite and finite single-hop networks, we obtain broad rate-stability conditions. We also consider symmetric finite multi-hop networks
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Job assignment in large-scale service systems with affinity relations Queueing Syst. (IF 1.114) Pub Date : 2019-10-10 Ellen Cardinaels; Sem C. Borst; Johan S. H. van Leeuwaarden
We consider load balancing in service systems with affinity relations between jobs and servers. Specifically, an arriving job can be assigned to a fast, primary server from a particular selection associated with this job or to a secondary server to be processed at a slower rate. Such job–server affinity relations can model network topologies based on geographical proximity, or data locality in cloud
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On a queueing-inventory system with advanced reservation and cancellation for the next K time frames ahead: the case of overbooking Queueing Syst. (IF 1.114) Pub Date : 2019-09-25 Dhanya Shajin; A. Krishnamoorthy; A. N. Dudin; Varghese C. Joshua; Varghese Jacob
We analyse the evolution of a system designed for reservation of some items in advance (for example, seats in aircrafts or trains or bus) by customers arriving at random moments. The reservation has to be done by the server in one of the K time frames. At the beginning of the pth time frame, the inventoried items in it (as well as those sold from it earlier) have life time distribution which is a p-fold
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Martingales and buffer overflow for the symmetric shortest queue model Queueing Syst. (IF 1.114) Pub Date : 2019-09-06 Danielle Tibi
A variant of the standard symmetric system of two parallel queues under the join-the-shortest-queue policy is introduced. Here, the shortest queue has service rate \(\mu _1\), while the longest queue has rate \(\mu _2\), where \(\mu _1 + \mu _2 = 1\). In the case of equality, both queues are served at rate 1 / 2. Each queue has capacity K, which may be finite or infinite, and the global Poisson arrival
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On mean-field (GI/GI/1) queueing model: existence and uniqueness Queueing Syst. (IF 1.114) Pub Date : 2019-09-04 A. Yu. Veretennikov
A mean-field extension of the queueing system (GI/GI/1) is considered. The process is constructed as a Markov solution of a martingale problem. Uniqueness in distribution is also established under a slightly different set of assumptions on intensities in comparison with those required for existence.
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Asymptotic behavior of a critical fluid model for a multiclass processor sharing queue via relative entropy Queueing Syst. (IF 1.114) Pub Date : 2019-09-03 Justin A. Mulvany; Amber L. Puha; Ruth J. Williams
This work concerns the asymptotic behavior of critical fluid model solutions for a multiclass processor sharing queue under general distributional assumptions. Such critical fluid model solutions are measure-valued functions of time. We prove that critical fluid model solutions converge to the set of invariant states as time goes to infinity, uniformly for all initial conditions lying in certain relatively
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Condition-based maintenance policies under imperfect maintenance at scheduled and unscheduled opportunities Queueing Syst. (IF 1.114) Pub Date : 2019-08-24 C. Drent; S. Kapodistria; J. A. C. Resing
Motivated by the cost savings that can be obtained by sharing resources in a network context, we consider a stylized, yet representative, model for the coordination of maintenance and service logistics for a geographic network of assets. Capital assets, such as wind turbines in a wind park, require maintenance throughout their long lifetimes. Two types of preventive maintenance are considered: planned
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The age-dependent random connection model Queueing Syst. (IF 1.114) Pub Date : 2019-07-20 Peter Gracar; Arne Grauer; Lukas Lüchtrath; Peter Mörters
We investigate a class of growing graphs embedded into the d-dimensional torus where new vertices arrive according to a Poisson process in time, are randomly placed in space and connect to existing vertices with a probability depending on time, their spatial distance and their relative birth times. This simple model for a scale-free network is called the age-based spatial preferential attachment network
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Admit or preserve? Addressing server failures in cloud computing task management Queueing Syst. (IF 1.114) Pub Date : 2019-07-17 Nadav Lavi; Hanoch Levy
Cloud computing task management has a critical role in the efficient operation of the cloud resources, i.e., the servers. The task management handles critical and complicated decisions, overcoming the inherent dynamic nature of cloud computing systems and the additional complexity due to the large magnitude of resources in such systems (tens of thousands of servers). Due to the fact that servers may
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Importance sampling for non-Markovian tandem queues using subsolutions Queueing Syst. (IF 1.114) Pub Date : 2019-07-16 Anne Buijsrogge; Pieter-Tjerk de Boer; Werner R. W. Scheinhardt
In this paper, we use importance sampling simulation to estimate the probability that the number of customers in a d-node GI|GI|1 tandem queue reaches some high level N in a busy cycle of the system. We present a state-dependent change of measure for a d-node GI|GI|1 tandem queue based on the subsolution approach, and we prove, under a mild conjecture, that this state-dependent change of measure gives
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Necessary conditions for the compensation approach for a random walk in the quarter-plane Queueing Syst. (IF 1.114) Pub Date : 2019-07-08 Yanting Chen; Richard J. Boucherie; Jasper Goseling
We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a countably infinite sum of geometric terms which individually satisfy the interior balance equations. We demonstrate that the compensation approach is the only method that may lead to such a type of invariant measure. In particular, we show that if a countably
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Redundancy scheduling with scaled Bernoulli service requirements Queueing Syst. (IF 1.114) Pub Date : 2019-06-22 Youri Raaijmakers; Sem Borst; Onno Boxma
Redundancy scheduling has emerged as a powerful strategy for improving response times in parallel-server systems. The key feature in redundancy scheduling is replication of a job upon arrival by dispatching replicas to different servers. Redundant copies are abandoned as soon as the first of these replicas finishes service. By creating multiple service opportunities, redundancy scheduling increases
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Admission control in a two-class loss system with periodically varying parameters and abandonments Queueing Syst. (IF 1.114) Pub Date : 2019-06-20 Gabriel Zayas-Cabán; Mark E. Lewis
Motivated by service systems, such as telephone call centers and emergency departments, we consider admission control for a two-class multi-server loss system with periodically varying parameters and customers who may abandon from service. Assuming mild conditions for the parameters, a dynamic programming formulation is developed. We show that under the infinite horizon discounted problem, there exists
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Networks of interacting stochastic fluid models with infinite and finite buffers Queueing Syst. (IF 1.114) Pub Date : 2019-06-18 Nikki Sonenberg; Peter G. Taylor
Stochastic fluid models have been widely used to model the level of a resource that changes over time, where the rate of variation depends on the state of some continuous-time Markov process. Latouche and Taylor (Queueing Syst 63:109–129, 2009) introduced an approach, using matrix analytic methods and the reduced load approximation for loss networks, to analyse networks of fluid models all driven by
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Optimal pricing for tandem queues with finite buffers Queueing Syst. (IF 1.114) Pub Date : 2019-06-11 Xinchang Wang; Sigrún Andradóttir; Hayriye Ayhan
We consider optimal pricing for a two-station tandem queueing system with finite buffers, communication blocking, and price-sensitive customers whose arrivals form a homogeneous Poisson process. The service provider quotes prices to incoming customers using either a static or dynamic pricing scheme. There may also be a holding cost for each customer in the system. The objective is to maximize either
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Bounds and limit theorems for a layered queueing model in electric vehicle charging Queueing Syst. (IF 1.114) Pub Date : 2019-05-29 Angelos Aveklouris; Maria Vlasiou; Bert Zwart
The rise of electric vehicles (EVs) is unstoppable due to factors such as the decreasing cost of batteries and various policy decisions. These vehicles need to be charged and will therefore cause congestion in local distribution grids in the future. Motivated by this, we consider a charging station with finitely many parking spaces, in which electric vehicles arrive in order to get charged. An EV has
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A stochastic analysis of a network with two levels of service Queueing Syst. (IF 1.114) Pub Date : 2019-05-25 Vianney Bœuf; Philippe Robert
In this paper, a stochastic model of a call center with a two-level architecture is analyzed. A first-level pool of operators answers calls, identifies, and handles non-urgent calls. A call classified as urgent has to be transferred to specialized operators at the second level. When the operators of the second level are all busy, the operator of first-level handling the urgent call is blocked until
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Strategic customer behavior in a two-stage batch processing system Queueing Syst. (IF 1.114) Pub Date : 2019-05-24 Olga Bountali; Antonis Economou
We consider a two-stage service system with batch processing. More specifically, customers arrive according to a Poisson process at the first stage of the system, where they do not receive any service, but wait until a number K of them are accumulated. Then, these K customers form a batch which is instantaneously transferred to the second stage where the batches are served sequentially, as single units
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An exact root-free method for the expected queue length for a class of discrete-time queueing systems Queueing Syst. (IF 1.114) Pub Date : 2019-05-17 A. Oblakova; A. Al Hanbali; R. J. Boucherie; J. C. W. van Ommeren; W. H. M. Zijm
For a class of discrete-time queueing systems, we present a new exact method of computing both the expectation and the distribution of the queue length. This class of systems includes the bulk-service queue and the fixed-cycle traffic-light (FCTL) queue, which is a basic model in traffic-control research and can be seen as a non-exhaustive time-limited polling system. Our method avoids finding the
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