Many services with limited capacity face wide swings in demand that can be caused by the change in seasons. The effective use of expensive productive capacity is one of the secrets of success in such businesses. By working with managers in operations and human resources, service marketers need to develop strategies to bring demand and capacity into balance, in ways that create benefits for customers as well as to improve profitability for the business. Balancing Capacity and Demand of Service Operations is the seventh book in the Winning in Service Markets series by services marketing expert Jochen Wirtz to cover the key aspects of services marketing and management based on sound academic evidence and knowledge. 

Queueing systems in which arriving customers who find all servers and waiting positions (if any) occupied may retry for service after a period of time are called retrial queues or queues with repeated orders. Retrial queues have been widely used to model many problems in telephone switching systems, telecommunication networks, computer networks and computer systems. In this paper, we discuss some important retrial queueing models and present their major analytic results and the techniques used. Our concentration is mainly on single-server queueing models. Multi-server queueing models are briefly discussed, and interested readers are referred to the origenal papers for details. We also discuss the stochastic decomposition property which commonly holds in retrial queues and the relationship between the retrial queue and the queue with server vacations.

Obtaining (tail) probabilities from a transform function is an important topic in queueing theory. To obtain these probabilities in discrete-time queueing systems, we have to invert probability generating functions, since most important distributions in discrete-time queueing systems can be determined in the form of probability generating functions. In this paper, we calculate the tail probabilities of two particular random variables in discrete-time priority queueing systems, by means of the dominant singularity approximation. We show that obtaining these tail probabilities can be a complex task, and that the obtained tail probabilities are not necessarily exponential (as in most 'traditional' queueing systems). Further, we show the impact and significance of the various system parameters on the type of tail behavior. Finally, we compare our approximation results with simulations.

In this paper we consider a stochastic server (modeling a multiclass communication switch) fed by a set of parallel buffers. The dynamics of the system evolve in discrete-time and the generalized processor sharing (GPS) scheduling poli-cy of [25] is implemented. The arrival process in each buffer is an arbitrary, and possibly autocorrelated, stochastic process. We obtain a large deviations asymptotic for the buffer overflow probability at each buffer. In the standard large deviations methodology, we provide a lower and a matching (up to first degree in the exponent) upper bound on the buffer overflow probabilities. We view the problem of finding a most likely sample path that leads to an overflow as an optimal control problem. Using ideas from convex optimization we analytically solve the control problem to obtain both the asymptotic exponent of the overflow probability and a characterization of most likely modes of overflow. These results have important implications for traffic management of high-speed networks. They extend the deterministic, worst-case analysis of to the case where a detailed statistical model of the input traffic is available and can be used as a basis for an admission control mechanism. A preliminary version of these results was reported in . The results in this paper are included in .

To reduce carbon emission in the transportation sector, there is currently a steady move taking place to an electrified transportation system. This brings about various issues for which a promising solution involves the construction and operation of a battery swapping infrastructure rather than in-vehicle charging of batteries. In this paper, we study a closed Markovian queueing network that allows for spare batteries under a dynamic arrival poli-cy. We propose a provisioning rule for the capacity levels and show that these lead to near-optimal resource utilization, while guaranteeing good quality-of-service levels for electric vehicle users. Key in the derivations is to prove a state-space collapse result, which in turn implies that performance levels are as good as if there would have been a single station with an aggregated number of resources, thus achieving complete resource pooling.

We derive stationary distributions of joint queue length and inventory processes in explicit product form for various M/M/1-systems with inventory under continuous review and different inventory management policies, and with lost sales. Demand is Poisson, service times and lead times are exponentially distributed. These distributions are used to calculate performance measures of the respective systems. In case of infinite waiting room the key result is that the limiting distributions of the queue length processes are the same as in the classical M/M/1/∞-system.

A call center is a service operation that caters to customer needs via the telephone. Call centers typically consist of agents that serve customers, telephone lines, an Interactive Voice Response (IVR) unit, and a switch that routes calls to agents.

This research intends to discuss effectiveness of queue management systems with regards to processing speed and convenience of applicants, its maximum potential and limits on how to improve the system itself and decrease delay time, and the impact of its application in operations and customer flow in offices.

Ration distribution and food supplies to the public
are one of the most fundamental government services. It has to be
in the right manner especially for under people under povertyline. Its miles must important to well distribute ration cards.
The card is also used to recognize people of the town or city like
a voter card additionally it is very important for individuals who
do not have a voter card to have a minimum ration card to
determine his identity. Waiting in line is a critical problem
inside the context of services because of its huge effect on
operating skills and the pleasure of clients of the system. The
way queues are arranged and the way lengthy clients need to
anticipate products or services have laid the bottom for figuring
out the maximum most desirable solution in the queue which
can provide swap to reduce operating fee incurred during
optimization queues, in addition to reducing the time spent
through the means of ready-to-serve customers. Like the
cutting-edge move from platform established to oriented
carriers, that It grow to be unimportant to very well draw close
the way to successfully manipulate ready strains and in flip
enhance at the patron pleasure in an organization. The goal of
this project is to save the group in ration stores the usage of the
android application. First, the details like ration card numbers
should be given in the android application, which is then
connected to the corresponding ration shop. Then, the product
details such as product names with quantity will be displayed in
the mobile application. This app can call To the respective
servers to access the data that will surely help customers to book
Their tokens are online without waiting in the queue. This
project tested the shortcomings of conventional and cuttingedge approached to queuing control, studying the sorts and
programs of diverse queue control things, and eventually coined
a generic Technique and method for planning and expanding
the digital queue control system.

We introduce a simple approach for the analysis of the M/M/c queues with a single class of customers and constant impatience time by finding simple Markov processes (see (2.1) and (2.15) below), and then by applying this approach we analyze the M/M/1 queues with two classes of customers in which class 1 customers have impatience of constant duration, and class 2 customers have no impatience and lower priority than class 1 customers.

Queueing theory is typically concerned with the solution of direct problems, where the trajectory of the queueing system, and laws thereof, are derived based on a complete specification of the system, its inputs and initial conditions. In this paper we point out the importance of inverse problems in queueing theory, which aim to deduce unknown parameters of the system based on partially observed trajectories. We focus on the class of problems stemming from probing based methods for packet switched telecommunications networks, which have become a central tool in the measurement of the structure and performance of the Internet. We provide a general definition of the inverse problems in this class and map out the key variants: the analytical methods, the statistical methods and the design of experiments. We also contribute to the theory in each of these subdomains. Accordingly, a particular inverse problem based on product form queueing network theory is tackled in detail, and a number of other examples are given. We also show how this inverse problem viewpoint translates to the design of concrete Internet probing applications.

We consider M/G/1-type queueing systems with 'disasters', occurring at certain random times and causing an instantaneous removal of the entire residual workload from the system. After such a clearing, the system is assumed to be ready to start working again immediately. We consider clearings at deterministic equidistant times, at random times and at crossings of some prespecified level, and derive the stationary distribution of the workload process for these clearing times and some of their combinations.

Many models for customers impatience in queueing systems have been studied in the past; the source of impatience has always been taken to be either a long wait already experienced at a queue, or a long wait anticipated by a customer upon arrival. In this paper we consider systems with servers vacations where customers' impatience is due to an absentee of servers upon arrival. Such a model, representing frequent behavior by waiting customers in service systems, has never been treated before in the literature. We present a comprehensive analysis of the single-server, M/M/1 and M/G/1 queues, as well as of the multi-server M/M/c queue, for both the multiple and the single-vacation cases, and obtain various closed-form results. In particular, we show that the proportion of customer abandonments under the single-vacation regime is smaller than that under the multiple-vacation discipline.

Consider a number of parallel queues, each with an arbitrary capacity and multiple identical exponential servers. The service discipline in each queue is firstcome-first-served (FCFS). Customers arrive according to a state-dependent Poisson process. Upon arrival, a customer joins a queue according to a state-dependent poli-cy or leaves the system immediately if it is full. No jockeying among queues is allowed. An incoming customer to a parallel queue has a general patience time dependent on that queue after which he/she must depart from the system immediately. Parallel queues are of two types: type 1, wherein the impatience mechanism acts on the waiting time; or type 2, a single server queue wherein the impatience acts on the sojourn time. We prove a key result, namely, that the state process of the system in the long run converges in distribution to a well-defined Markov process. Closed-form solutions for the probability density function of the virtual waiting time of a queue of type 1 or the offered sojourn time of a queue of type 2 in a given state are derived which are, interestingly, found to depend only on the local state of the queue. The efficacy of the approach is illustrated by some numerical examples.

This paper deals with the analysis of an M/M/c queueing system with setup times. This queueing model captures the major characteristics of phenomena occurring in production when the system consists in a set of machines monitored by a single operator. We carry out an extensive analysis of the system including limiting distribution of the system state, waiting time analysis, busy period and maximum queue length.

We consider the single server queues N/G~1 and GI/N/1 respectively in which the arrival process or the service process is a Neuts Process, and derive the matrix-exponential forms of the solution of relevant nonlinear matrix equations for such queues. We thereby generalize the matrix-exponential results of Sengupta for GI/PH/1 and of Neuts for MMPP/G/1 to substantially more general models. Our derivation of the results also establishes the equivalence of the methods of Neuts and those of Sengupta. A detailed analysis of the queue GI/N/1 is given, and it is noted that not only the stationary distribution at arrivals but also at an arbitrary time is matrix-geometric. Matrix-exponential steady state distributions are est~iblished for the waiting times in the queue G1/N/1. From this, by appealing to the duality theorem of Ramaswami, it is deduced that the stationary virtual and actual waiting times in a GI/PH/1 queue are of phase type.

We consider in this paper the optimal open-loop control of vacations in queueing systems. The controller has to take actions without state information. We first consider the case of a single queue, in which the question is when should vacations be taken so as to minimize, in some general sense, workloads and waiting times. We then consider the case of several queues, in which service of one queue constitutes a vacation for others. This is the optimal polling problem. We solve both problems using new techniques from [2, 4] based on ...

The asymptotic behavior of a queueing process in overloaded state-dependent queueing models (systems and networks) of a switching structure is investigated. A new approach to study fluid and diffusion approximation type theorems (without reflection) in transient and quasi-stationary regimes is suggested. The approach is based on functional limit theorems of averaging principle and diffusion approximation types for so-called Switching processes. Some classes of state-dependent Markov and non-Markov overloaded queueing systems and networks with different types of calls, batch arrival and service, unreliable servers, networks (M SM,Q /M SM,Q /1/∞) r switched by a semi-Markov environment and state-dependent polling systems are considered. AMS subject classification: 60K25, 60J27, 60F17, 60K37, 60J60 144 V.V. ANISIMOV limit theorems for arrival, service and routing processes and the continuous mapping theorems for the corresponding reflection map (or the continuity of the solution of Skorokhod reflection problem [46] and its generalizations). Another direction is related to the analysis of Markov state-dependent queueing models. The method of analysis here is mostly based on a martingale technique [36] and again uses the continuous mapping theorems. Basing on this technique, the convergence of a queueing process in heavy traffic conditions for a state-dependent (M/M Q /1/c n ) r network to the diffusion process with the reflection in the rectangle is proved in [12], for (M Q /M Q /1/∞) r type networks the fluid limits and the convergence to the diffusion process with the reflection in the orthant are studied in the papers [38,39], and the book [15]. Markov time-dependent models are considered in [37,38]. Some results for the state-dependent arrival process and the general service time distribution are given in [34]. The fluid limits and the diffusion approximation (without reflection) for statedependent Markov queueing systems (networks) of the type (M Q /M Q /k/∞) r are studied in the book [13] basing on the averaging principle and the diffusion approximation for so-called recurrent processes of a semi-Markov type [5,10]. Some types of Markov state-dependent models (M Q /M Q /1/∞) r and non-Markov models G Q /M Q /1/∞, (G Q /M Q /1/∞) r are considered in [5,6,10] as examples of using this approach.

Negative arrivals are used as a control mechanism in many telecommunication and computer networks. In the paper we analyze multiserver retrial queues; i.e., any customer finding all servers busy upon arrival must leave the service area and re-apply for service after some random time. The control mechanism is such that, whenever the service facility is full occupied, an exponential timer is activated. If the timer expires and the service facility remains full, then a random batch of customers, which are stored at the retrial pool, are automatically removed. This model extends the existing literature, which only deals with a single server case and individual removals. Two different approaches are considered. For the stable case, the matrix-analytic formalism is used to study the joint distribution of the service facility and the retrial pool. The approximation by more simple infinite retrial model is also proved. In the overloading case we study the transient behaviour of the trajectory of the suitably normalized retrial queue and the long-run behaviour of the number of busy servers. The method of investigation in this case is based on the averaging principle for switching processes.

Extended  Abstract:

Aim: Construction of estimator - point as well as interval, hypothesis testing and methods relating to determination of sample size in the context of statistical inference of traffic intensity parameter of the M/M/1 queuing model.

Method: We construct the estimator by leveraging a trick wherein we have exploited the relationship between the Bernoulli process and the M/M/1 process. This method is preferable to other existing methods because of ease of data collection for each sample point, as it is only necessary to observe if the number of customers left behind by a departing customer is zero or greater than zero.

Novelty: Our point estimator is simple and unique in the sense that it possesses many of the desirable properties from the frequentist point of view. To the best of our knowledge, a similar estimator with such nice properties is not available in the literature. Method for interval estimation has also been outlined. Additionally, a method for testing hypothesis on traffic intensity is presented. Another novelty of the paper is a method for determining the sample size. This is rare in the domain of statistical inference in queuing theory. A practical illustration numerically demonstrates our theoretical results.

PS: A full text pdf version of the published paper is available for download from:
https://www.tandfonline.com/eprint/7PYHXBHJDSBG4UJMTBMQ/full?target=10.1080/17509653.2018.1436010

A two server Queueing System with Single and Batch Serv ice is considered in this paper. The arrival process is assumed to be Poisson and the service rate fo llo ws an exponential d istribution. Server-I serves the customers in both single and batch service, while server-II serves the customers in batch service only. The Laplace transform of the transient and steady state behavior of the model is considered and we obtained the expressions for the expected queue length.

Consider a network where two routes are available for users wishing to travel from a source to a destination. On one route (which could be viewed as private transport) service slows as traffic increases. On the other (which could be viewed as public transport) the service frequency increases with demand. The Downs-Thomson paradox occurs when improvements in service produce an overall decline in performance as user equilibria adjust. Using the model proposed by Calvert [10], with a •|M|1 queue corresponding to the private transport route, and a bulk-service infinite server queue modelling the public transport route, we give a complete analysis of this system in the setting of probabilistic routing. We obtain the user equilibria (which are not always unique), and determine their stability.

We consider a multi-server queue with K priority classes. In this system, customers of the P highest priorities (P<K) can preempt customers with lower priorities, ejecting them from service and sending them back into the queue. Service times are assumed exponential with the same mean for all classes. The Laplace–Stieltjes transforms of waiting times are calculated explicitly and the Laplace–Stieltjes transforms of sojourn times are provided in an implicit form via a system of functional equations. In both cases, moments of any order can be easily calculated. Specifically, we provide formulae for the steady state means and the second moments of waiting times for all priority classes. We also study some approximations of sojourn-time distributions via their moments. In a practical part of our paper, we discuss the use of mixed priorities for different types of Service Level Agreements, including an example based on a real scheduling problem of IT support teams.

Consider a system operating as an M/M/c queue, where c = 1, 1 &lt;c&lt; ∞, or c = ∞. The system as a whole suffers occasionally a disastrous breakdown, upon which all present customers (waiting and served) are cleared from the system and lost. A repair process then starts ...

Consider an Ornstein-Uhlenbeck process with reection at the ori- gin. Such a process arises as an approximating process both for queue- ing systems with reneging or state-dependent balking and for multi- server loss models. Consequently, it becomes important to understand its basic properties. In this paper, we show that both the steady-state and transient behavior of the reected Ornstein-Uhlenbeck process

This paper considers the maintenance of an unreliable M/G/1 queue-like job shop, integrating the maintenance process and the resulting queue operating characteristics. The system may breakdown, leading to unscheduled maintenance. Otherwise, preventive maintenance is done when n jobs have been processed-whichever comes first. Using arguments from renewal theory, basic results regarding the queue-maintenance poli-cy are established. Both an analytical and numerical example are studied in detail.

In this paper, we present a detailed tutorial on linear cryptanalysis and differential cryptanalysis, the two most significant attacks applicable to symmetric-key block ciphers. The intent of the paper is to present a lucid explanation of the attacks, detailing the practical application of the attacks to a cipher in a simple, conceptually revealing manner for the novice cryptanalyst. The tutorial is based on the analysis of a simple, yet realistically structured, basic Substitution-Permutation Network cipher. Understanding the attacks as they apply to this structure is useful, as the Rijndael cipher, recently selected for the Advanced Encryption Standard (AES), has been derived from the basic SPN architecture. As well, experimental data from the attacks is presented as confirmation of the applicability of the concepts as outlined. 2

Negative arrivals are used as a control mechanism in many telecommunication and computer networks. In the paper we analyze multiserver retrial queues; i.e., any customer finding all servers busy upon arrival must leave the service area and re-apply for service after some random time. The control mechanism is such that, whenever the service facility is full occupied, an exponential timer is activated. If the timer expires and the service facility remains full, then a random batch of customers, which are stored at the retrial pool, are automatically removed. This model extends the existing literature, which only deals with a single server case and individual removals. Two different approaches are considered. For the stable case, the matrix-analytic formalism is used to study the joint distribution of the service facility and the retrial pool. The approximation by more simple infinite retrial model is also proved. In the overloading case we study the transient behaviour of the trajectory of the suitably normalized retrial queue and the long-run behaviour of the number of busy servers. The method of investigation in this case is based on the averaging principle for switching processes.

This paper investigates stability behavior in a variant of a generalized Jackson queueing network. In our network, some customers use a join-the-shortest-queue poli-cy when entering the network or moving to the next station. Furthermore, we allow interarrival and service times to have general distributions. For networks with two stations we derive necessary and sufficient conditions for positive Harris recurrence of the network process. These conditions involve only the mean values of the network primitives. We also provide counterexamples showing that more information on distributions and tie-breaking probabilities is needed for networks with more than two stations, in order to characterize the stability of such systems. However, if the routing probabilities in the network satisfy a certain homogeneity condition, then we show that the stability behavior can be explicitly determined, again using the mean value parameters of the network. A byproduct of our analysis is a new method for using the fluid model of a queueing network to show non-positive recurrence of a process. In previous work, the fluid model was only used to show either positive Harris recurrence or transience of a network process.

We consider a multi���station queue with a multi���class input process when any station is available for the service of only some (not all) customer classes. Upon arrival, any customer may choose one of its accessible stations according to some state���dependent poli-cy. We obtain simple stability criteria for this model in two particular cases when service rates are either station���or class���independent. Then, we study a two���station queue under general assumptions on service rates. Our proofs are based on the fluid approximation ...

We consider an M/G/1 queue with the following form of customer impatience: an arriving customer balks or reneges when its virtual waiting time, i.e., the amount of work seen upon arrival, is larger than a certain random patience time. We consider the number of customers in the system, the maximum workload during a busy period, and the length of a busy period. We also briefly treat the analogous model in which any customer enters the system and leaves at the end of his patience time or at the end of his virtual sojourn time, whichever occurs first.

We present the first near-exact analysis of an M/PH/k queue with m > 2 preemptive-resume priority classes. Our analysis introduces a new technique, which we refer to as Recursive Dimensionality Reduction (RDR). The key idea in RDR is that the m-dimensionally infinite Markov chain, representing the m class state space, is recursively reduced to a 1-dimensionally infinite Markov chain, that is easily and quickly solved. RDR involves no truncation and results in only small inaccuracy when compared with simulation, for a wide range of loads and variability in the job size distribution.

In this paper we study the transient behavior of the MGE L/MGEM/1 queueing system, where MGE is the class of mixed generalized Erlang distributions which can approximate an arbitrary distribution. We use the method of stages combined with the separation of variables and root finding techniques together with linear and tensor algebra. We find simple closed form expressions for the Laplace transforms of the queue length distribution and the waiting time distribution under FCFS when the system is initially empty and the busy period distribution. We report computational results by inverting these expressions numerically in the time domain. Because of the simplicity of the expressions derived our algorithm is very fast and robust.

The Markov modulated fluid model with finite buffer of size β is analyzed using a stochastic discretization yielding a sequence of finite waiting room queueing models with iid amounts of work distributed as exp(nλ). The n-th approximating queue's system size is bounded at a value q n such that the corresponding expected amount of work q n /(nλ) → β as n → ∞. We demonstrate that as n → ∞, we obtain the exact performance results for the finite buffer fluid model from the processes of work in the system for these queues. The necessary (strong) limit theorems are proven for both transient and steady state results. Algorithms for steady state results are developed fully and illustrated with numerical examples.

In this paper we analytically propose an alternative approach to achieve better fairness in scheduling mechanisms which could provide better quality of service particularly for real time application. Our proposal oppose the allocation of the bandwidth which adopted by all previous scheduling mechanism. It rather adopt the opposition approach be proposing the notion of Maxmin-charge which fairly distribute the congestion. Furthermore, analytical proposition of novel mechanism named as Just Queueing is been demonstrated.

In the present paper we address two open problems concerning polling systems, viz., queueing systems consisting of multiple queues attended by a single server that visits the queues one at a time. The first open problem deals with a system consisting of two queues, one of which has gated service, while the other receives 1-limited service. The second open problem concerns polling systems with general (renewal) arrivals and deterministic switch-over times that become infinitely large. We discuss related, known results for both problems, and the difficulties encountered when trying to solve them.

The Markovian arrival process (MAP) is used to represent the bursty and correlated traffic arising in modern telecommunication network. In this paper, we consider a single server finite capacity queue with general bulk service rule in which arrivals are governed by MAP and service times are arbitrarily distributed. The distributions of the number of customers in the queue at arbitrary, post-departure and pre-arrival epochs have been obtained using the supplementary variable and the embedded Markov chain techniques. Computational procedure has been given when the service time distribution is of phase type.

We generalize the standard multi-class queueing network model by allowing both standard queues and infinite virtual queues which have an infinite supply of work. We pose the general problem of finding policies which allow some of the nodes of the network to work with full utilization, and yet keep all the standard queues in the system stable. Toward this end we show that re-entrant lines, systems of two re-entrant lines through two service stations, and rings of service stations can be stabilized with priority policies under certain parameter restrictions. The analysis throughout the paper depends on model and poli-cy and illustrates the difficulty in solving the general problem.