Queueing Systems

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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 original 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.

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 policy. 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.

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.

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 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 ...

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.

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

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

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 policy 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 policy. 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 ...

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.