A discrete-time retrial queue with negative customers and unreliable server

This paper treats a discrete-time single-server retrial queue with geometrical arrivals of both positive and negative customers in which the server is subject to breakdowns and repairs. Positive customers who find sever busy or down are obliged to leave the service area and join the retrial orbit. They request service again after some random time. If the server is found idle or busy, the arrival of a negative customer will break the server down and simultaneously kill the positive customer under service if any. But the negative customer has no effect on the system if the server is down. The failed server is sent to repair immediately and after repair it is assumed as good as new. We analyze the Markov chain underlying the queueing system and obtain its ergodicity condition. The generating functions of the number of customers in the orbit and in the system are also obtained along with the marginal distributions of the orbit size when the server is idle, busy or down. Finally, some numerical examples show the influence of the parameters on some crucial performance characteristics of the system.     

A discrete-time retrial queueing system with recurrent customers

We consider a discrete-time single-server retrial queue with general service times and two classes of customers: transit and a fixed number of recurrent customers. After service completion, recurrent customers always return to the orbit and transit customers leave the systems forever. In this work we study the influence of recurrent customers. This structure appears in many applications on computer and communication networks, but also has theoretical interest. The explicit expressions of generating functions of the stationary distribution of the Markov chain are given. We also provide the main reliability indexes and numerical examples with the use of discrete Fourier transform inversion.     

A new solution for a queueing model of a manufacturing cell with negative customers under a rotation rule

In this paper, we consider a queueing model extension for a manufacturing cell composed of a machining center and several parallel downstream production stations under a rotation rule. A queueing model is extended with the arrival processes of negative customers to capture failures of production stations, reorganization of works and disasters in the manufacturing cell. We present an exact solution for the steady-state probabilities of the proposed queueing model. The solution does not require the approximation of the infinite sum. In addition, it provides an alternative way to compute the rate matrix for the matrix-geometric method as well.     

Stability of a two-class two-server retrial queueing system

We consider a two-class two-server retrial queueing system. Customers of each class arrive according to a Poisson process and the service times of each class of customers are assumed to be exponentially distributed with service rates depending on both the customer’s class and the servers. We provide stability and instability conditions for this retrial queueing system.     

A discrete-time single-server queue with a modified N -policy

We consider a discrete-time single-server queue where the idle server waits for reaching a level N in the queue size to start a batch service of N messages, although the following arrivals during the busy period receive single services. We find the stationary distributions of the queue and system lengths as well as some performance measures. The vacation and busy periods of the system and the number of messages served during a busy period are also analyzed. The stationary distributions of the time spent waiting in the queue and in the system are studied too. Finally, a total expected cost function is developed to determine the optimal operating N-policy at minimum cost.     

Analysis of the discrete-time Geo/G/1 working vacation queue and its application to network scheduling

In this paper we present an exact steady-state analysis of a discrete-time Geo/G/1 queueing system with working vacations, where the server can keep on working, but at a slower speed during the vacation period. The transition probability matrix describing this queuing model can be seen as an M/G/1-type matrix form. This allows us to derive the probability generating function (PGF) of the stationary queue length at the departure epochs by the M/G/1-type matrix analytic approach. To understand the stationary queue length better, by applying the stochastic decomposition theory of the standard M/G/1 queue with general vacations, another equivalent expression for the PGF is derived. We also show the different cases of the customer waiting to obtain the PGF of the waiting time, and the normal busy period and busy cycle analysis is provided. Finally, we discuss various performance measures and numerical results, and an application to network scheduling in the wavelength division-multiplexed (WDM) system illustrates the benefit of this model in real problems.     

A queueing system with batch arrival of customers in sessions

This paper describes and analyzes a single-server queueing model with a finite buffer and session arrivals. Generation of the sessions is described by the Markov Arrival Process (MAP). Arrival of the groups of the requests within any admitted session is described by the Terminating Batch Markov Arrival Process (TBMAP). Service time of the request has Phase (PH) type distribution. The number of the sessions that can be simultaneously admitted to the system is under control.     

Modeling and optimization of a product-service system with additional service capacity and impatient customers

Product-service system is a business model, in which a company offers a mix of products and services to maintain competitive edge, satisfy customer needs, and produce lower environmental impact than that produced by a traditional business model. This paper studies the modeling and optimization problems for a basic product-service system from the view point of operation management. The proposed system, modeled as a block structure Markov chain, features additional service capacity and impatient customers. The Matrix geometric methodology is applied to obtain the stationary distribution of the system. The performance indices for the system are derived based on the distribution, and the sensitivity of the performance with respect to the parameters is considered by numerical experiments. Meanwhile, the decision process of obtaining the optimal sets of additional service capacity opening threshold and the base store level is discussed from the point of view of profit optimization We propose algorithms to solve the problem, which are shown to be effective and efficiency by numerical experiments. The studies of the sensitivity of the optimal decision to the parameters propose some insight on system demand management and system improvement.     

基于1坚持指数退避算法的时隙CSMA/CD协议的排队模型的建立与分析

建立了1坚持指数退避算法的CSMA/CD协议的离散时间排队模型,基于该模型分析了网络吞吐量(S)、等待时间(W)等性能指标,并通过建立相应的马尔可夫链(MarkovChain),计算了信道忙的概率及产生冲突的概率。     

MMAP|M|N queueing system with impatient heterogeneous customers as a model of a contact center

A multi-server queueing system with infinite buffer and impatient heterogeneous customers as a model of a contact center that processes incoming calls (priority customers) and e-mail requests (non-priority customers) is investigated. The arrival flow is described by a Marked Markovian Arrival Process (MMAP). The service time of priority and non-priority customers by a server has an exponential distribution with different parameters. The steady state distribution of the system is analyzed. Some key performance measures are calculated. The Laplace–Stieltjes transforms of the sojourn and waiting time distribution are derived. The problem of optimal choice of the number of contact center agents under the constraint that the average waiting time of e-mail requests does not exceed a predefined value is numerically solved.     

Performance analysis of an M/G/1 queueing system under Bernoulli vacation schedules with server setup and close down periods

This paper is concerned with the analysis of a single server queueing system subject to Bernoulli vacation schedules with server setup and close down periods. An explicit expression for the probability generating function of the number of customers present in the system is obtained by using imbedded Markov chain technique. The steady state probabilities of no customer in the system at the end of vacation termination epoch and a service completion epoch are derived. The mean number of customers served during a service period and the mean number of customers in the system at an arbitrary epoch are investigated under steady state. Further, the Laplace-Stieltjes transform of the waiting time distribution and its corresponding mean are studied. Numerical results are provided to illustrate the effect of system parameters on the performance measures.     

A finite source multi-server inventory system with service facility

In this article, we study a continuous review retrial inventory system with a finite source of customers and identical multiple servers in parallel. The customers arrive according a quasi-random process. The customers demand unit item and the demanded items are delivered after performing some service the duration of which is distributed as exponential. The ordering policy is according to (s, S) policy. The lead times for the orders are assumed to have independent and identical exponential distributions. The arriving customer who finds all servers are busy or all items are in service, joins an orbit. These orbiting customer competes for service by sending out signals at random times until she finds a free server and at least one item is not in the service. The inter-retrial times are exponentially distributed with parameter depending on the number of customers in the orbit. The joint probability distribution of the number of customer in the orbit, the number of busy servers and the inventory level is obtained in the steady state case. The Laplace–Stieltjes transform of the waiting time distribution and the moments of the waiting time distribution are calculated. Various measures of stationary system performance are computed and the total expected cost per unit time is calculated. The results are illustrated numerically.     

A Kalman–Yakubovich–Popov-type lemma for systems with certain state-dependent constraints

In this note, a result is presented that may be considered an extension of the classical Kalman–Yakubovich–Popov (KYP) lemma. Motivated by problems in the design of switched systems, we wish to infer the existence of a quadratic Lyapunov function (QLF) for a nonlinear system in the case where a matrix defining one system is a rank-1 perturbation of the other and where switching between the systems is orchestrated according to a conic partitioning of the state space Rⁿ. We show that a necessary and sufficient condition for the existence of a QLF reduces to checking a single constraint on a sum of transfer functions irrespective of problem dimension. Furthermore, we demonstrate that our conditions reduce to the classical KYP lemma when the conic partition of the state space is Rⁿ, with the transfer function condition reducing to the condition of Strict Positive Realness.     

Characterization of a SAG‐InGaN/AlGaN LED by mixed‐source HVPE with a multi‐sliding boat system

Abstract— The selective area growth (SAG) of a InGaN/AlGaN light‐emitting diode (LED) is performed by using mixed‐source hydride vapor‐phase epitaxy (HVPE) with a multi‐sliding boat system. The SAG‐InGaN/AlGaN LED consists of a Si‐doped AlGaN cladding layer, an InGaN active layer, a Mg‐doped AlGaN cladding layer, and a Mg‐doped GaN capping layer. The carrier concentration of the n‐type Al_xGa_1?xN (x ～ 16%) cladding layer depends on the amount of poly‐Si placed in the Al‐Ga source. The carrier concentration is varied from 2.0 × 10¹⁶ to 1.1 × 10¹⁷ cm^?3. Electroluminescence (EL) characteristics show an emission peak wavelength at 426 nm with a full width at half‐maximum (FWHM) of approximately 0.47 eV at 20 mA. It was found that the mixed‐source HVPE method with a multi‐sliding boat system is a candidate growth method for III‐nitride LEDs.     

Robust filtering for 2-D discrete-time linear systems with convex-bounded parameter uncertainty

This paper is concerned with the problems of robust H_∞ and H₂ filtering for 2-dimensional (2-D) discrete-time linear systems described by a Fornasini-Marchesini second model with matrices that depend affinely on convex-bounded uncertain parameters. By a suitable transformation, the system is represented by an equivalent difference-algebraic representation. A parameter-dependent Lyapunov function approach is then proposed for the design of 2-D stationary discrete-time linear filters that ensure either a prescribed H_∞ performance or H₂ performance for all admissible uncertain parameters. The filter designs are given in terms of linear matrix inequalities. Numerical examples illustrate the effectiveness of the proposed filter design methods.     

Standby system with general repair, reboot delay, switching failure and unreliable repair facility—A statistical standpoint

This study statistically examines an availability system with reboot delay, standby switching failures and an unreliable repair facility, which consists of two active components and one warm standby. The time-to-failure and the reboot time are assumed to be exponentially distributed. The repair time of the service station and the time-to-repair of component are assumed to be generally distributed. A consistent and asymptotically normal estimator of availability of such a repairable system is developed. Based on this estimator, interval estimation and testing hypothesis are performed by using logit transformation. To implement the simulation inference for the system availability, two repair-time distributions, lognormal and Weibull distributions, are used. Three Weibull distributions characterized by distinct shape parameters are considered. Finally, all simulation results are displayed as appropriate tables and curves to reveal the performance of the statistical inference procedures.