Queueing theory

This chapter concerns the mathematical modeling and analysis of secondary (or auxiliary) storage devices, which often comprise the principal bottleneck in the overall performance of computer systems. The presentation begins with descriptions of the more important devices, such as disks and drums, and a general discussion of related queueing models. Server motion and dependent successive services are salient features of these models. Widely used, generic results and methods are presented and then applied to specific devices. The chapter concludes with a discussion of open problems and desirable extensions of the basic models. t This is an update of the identically named chapler in H. Takagi (Ed.): Stochastic Analysis Of Computer and ConrmJJlIicaticm Systems, Elsevier Science Pub!. B.V. 1990. ,*Currently at the Department of Computer Science, Purdue University, W. Lafayelle, IN 47907. ' " ' " t-'1,'x"j ...' x"M 1 M' X XI~'x"Mã nd similarly the pgf UI(Z). It is easier to proceed directly in lenns of the pgfs, exploiting the independence of services, inter-arrival and switching times. The definition of C i leads to a relation uacross" a switching time:

A simple MP system consisting of an input-output facility and a central processor is modeled as a two-parameter Markov chain. The conditions for stability are demonstrated, and the steady-state joint probabilities are calculated explicitly. Various priority and capacity assignments result in radically different analytical situations, some of which have been considered in the literature. The present work treats a version that was considered for a time intractable. This paper emphasizes the analytical properties of the probability-generating functions and a method to solve a resultant functional equation. The numerical results display the importance of dependence between variables in the model.

In his paper, Pearce presents a method for determining the stationary probabilities of a G/Mt/1 system, the service mechanism being such that it operates regardless of whether or not customers are present. This note is an attempt to correct his results.

In this paper we adopt the view of auxiliary stor&g9 devices in a oomputer system-typically disks and drums -as service facilities, responding to data transmission requests from active tasks •. The enormous disparities in processing rates between the different system oompoI18nts give rise to a variety of oongestion phenomena. We desoribe the physical properties of ; these devices and various methods of scheduling their activities with their motivations. Several examples are presented, where queueing-theoretical analysis was found a useful too,l; some open problems are suggest,d.

Capacity decisions in service operations often involve a trade-off between the operating cost and the service level offered to customers. Although the cost of attaining a pre-specified service level has been well-studied, there isn't much research studying how customer service levels affect revenue and profit. This paper conducts an empirical study to analyze how waiting in queue in the context of a retail store affects customer purchasing behavior. Our methodology uses a novel technology based on digital imaging to record periodic information about the queuing system. Our econometric method uses queuing theory combining these data with point-of-sales information to estimate the effect of queues on purchases. We find that waiting in queue has a non-linear impact on purchase incidence and that customers appear to focus mostly on the length of the queue, without adjusting enough for the speed at which the line moves. We also find that customers' sensitivity to waiting is heterogeneous and negatively correlated with price sensitivity. These empirical findings have important implications for service design, staffing and pricing. First, pooling multiple queues into a single queue may increase the length of the queue observed by customers and thereby lead to an increase in lost sales. Second, the model can be used to make staffing decisions, balancing labor costs with revenues. Third, we show that the relationship between price and waiting sensitivity is an important factor for pricing decisions in a multi-product category when congestion effects are present.

The Internet of Things (IoT) paradigm, has opened up the possibility of using the ubiquity of small devices to route information without the necessity of being connected to a Wide Area Network (WAN). Use cases of IoT devices sending updates that are routed and delivered by other IoT devices have been proposed in the literature. In this paper we focus on receivers only interested in the freshest updates from the sending device. In particular, the dynamic network created by routing/gossiping through small devices creates the possibility of delivering updates out of order. Thus, the entire process can be studied well through a queueing system with infinitely many servers, all serving updates with a random service time. Age of Information (AoI) was proposed as the main metric to measure information freshness. We study the amount of time that the AoI is over a certain threshold at the receiver end as a Quality of Service (QoS) measure, called update outage probability. Particularly, give...

In many IoT applications, sensor data is sent remotely to be processed, but only the freshest result is of interest. In this paper we investigate a feedback mechanism that aborts the processing of stale data at the remote end to reduce the load and save costs. The process is approximated by an M/M/∞ queueing system with a feedback loop. We find the exact expression of the average computational time saved and show that with the feedback loop in place the computation time per CPU can be cut up to 25%, making the technique very promising.

Performance modeling is an important topic in capacity planning and overload control for web servers. We present an M/GNK*PS queueing model of a web server. The arrival process of HTTP requests is assumed to he Poissonian and the semce discipline is processor sharing. The total number of requests that can he processed at one t i e is l i t e d to K. We obtain closed form expressions for web sewer performance metrics such as average response time, throughput and hlofking probability. The average of the service time requirement and the limit of the number of requests being Served are model parameters. The parameters are estimated by maximizing the log-likelihood function d the measumd average response time. Compared to other models, our model is conceptually simple and it is easy to estimate model parameters. The model has been validated thmngh measurements in our lab. The performance metrics predicted by the model fit well to the experimental outcome.

In order to deliver service in quality specially in banking system the queuing model was appropriate in order to suggest waiting time, service rate and etc for efficient service delivery of better implementation of banking system. Comparative study of two selected banks (Commercial Bank of Ethiopia & Dashen Bank) in Wolaita zone of Ethiopia was investigated. The queuing model was employed for both banking system in order to measure the behavioral queuing characteristics of customers in terms of their arrival and service rate respectively. The data for the arrival and service rate of the two banks were collected by observation methods for two days of a week simultaneously. The result revealed that on average 10.2 and 8.6 customers arrive and served per hours, respectively in Commercial Bank of Ethiopia Tona branch.

A number of nonlinear programming algorithms are proposed to obtain the approximate solutions for nonproduct form multiclass queueing network models, as well as priority queueing networks. Using sensitivity analysis, we develop an efficient iterative technique for closed queueing networks. We compare the approximate solutions obtained from our approach with the global balance solution. Examples illustrate the accuracy of the approximation, and compare the efficiency of the different optimization methods we have implemented.

This paper analyzes the performance of a MAC scheme for wireless local area networks (WLANs) that makes use of distributed queues to improve radio channel utilization. Analytical values for the maximum throughput performance are derived as a function of the system parameters. The obtained results show that the proposed scheme outperforms the legacy 802.11 MAC protocol in terms of maximum stable throughput. This benefit is obtained from eliminating back-off periods and collisions in data packet transmissions while minimizing the needed control overhead. The proposal also makes performance to be independent of the number of nodes transmitting in the system and provides stability for high load conditions.

This paper introduces an approach for determining the performability of repairable degradable systems based upon combining Deterministic and Stochastic Petri Nets and product-form queueing network models. The novel feature of the proposed modeling technique lies in its detailed representation of the transient behavior during a reconfiguration process. The reconfiguration time of a task and the rebooting time of a processor are represented in the model as deterministic delays. We employ a hierarchical decomposition method in order to reduce the computational effort of the solution. The employment of this decomposition technique leads to an exact solution because there is no interaction between a flowequivalent transition and the complementary subnet of the aggregated DSPN. To illustrate the modeling technique proposed in this paper we consider a loosely-coupled multicomputer system consisting of two computers and three disk systems.

This paper introduces an approach for determining the performability of repairable degradable systems based upon combining Deterministic and Stochastic Petri Nets and product-form queueing network models. The novel feature of the proposed modeling technique lies in its detailed representation of the transient behavior during a reconfiguration process. The reconfiguration time of a task and the rebooting time of a processor are represented in the model as deterministic delays. We employ a hierarchical decomposition method in order to reduce the computational effort of the solution. The employment of this decomposition technique leads to an exact solution because there is no interaction between a flowequivalent transition and the complementary subnet of the aggregated DSPN. To illustrate the modeling technique proposed in this paper we consider a loosely-coupled multicomputer system consisting of two computers and three disk systems.

The overpopulated cities complain about the congestion and the pollution made by conventional transport system. The Vehicle Sharing Systems come as a great solution for these problems. The vehicles can be Electrical Cars, Electrical Scooters, Electrical Bikes or conventional Bikes. Vélib' one of the biggest Bike Sharing System (BSS) with 18000 bikes, is operational in Paris since 2007. An Electrical Scooter Sharing System is in a testing phase in Paris (Cityscoot) and is planned to be fully operational in the middle of 2016. Already many cities, having such operational system, need tools to manage it and make it more efficient. The performance evaluation is needed to get insights and make strategic and operational decisions. We model the bike sharing system using the queueing theory, precisely the Closed Queueing Networks (CQN). For the derived class of network, the steady-state probability of the states of the network model has a product form solution. This allows us to use the Mean Value Analysis (MVA) to derive the mean performances in steady state. The mean number of bikes in the different stations is calculated as well as the availability of free bikes in a station. The utilisation rate of bikes is also deduced. Finally some strategic insights were deduced to get better performance of the system.

The overpopulated cities complain about the congestion and the pollution made by conventional transport system. The Vehicle Sharing Systems come as a great solution for these problems. The vehicles can be Electrical Cars, Electrical Scooters, Electrical Bikes or conventional Bikes. Vélib' one of the biggest Bike Sharing System (BSS) with 18000 bikes, is operational in Paris since 2007. An Electrical Scooter Sharing System is in a testing phase in Paris (Cityscoot) and is planned to be fully operational in the middle of 2016. Already many cities, having such operational system, need tools to manage it and make it more efficient. The performance evaluation is needed to get insights and make strategic and operational decisions. We model the bike sharing system using the queueing theory, precisely the Closed Queueing Networks (CQN). For the derived class of network, the steady-state probability of the states of the network model has a product form solution. This allows us to use the Mean Value Analysis (MVA) to derive the mean performances in steady state. The mean number of bikes in the different stations is calculated as well as the availability of free bikes in a station. The utilisation rate of bikes is also deduced. Finally some strategic insights were deduced to get better performance of the system.

Background Tuberculosis (TB) remains a threat to public health globally and is one of the top infectious killer diseases in Africa and Asia. The government and international partners have strategically intervened by cascading chest radiography (CXR) to identify, manage, and monitor treatments outcomes. However, patient have reportedly been dissatisfied with the quality of CXR screening services provided, raising complains that spans across quality of care, waiting times, communication levels, staff attitudes, and treatment outcomes. Aim, Settings, and Design Coming at this present time when the major focus in health care is on improving patients' care and experience, this study aims to ascertain the performance of queue management system (QMS) use for CXR-TB screening in Nigeria as well as its acceptability; adopting quantitative research design. Materials and Methods Questionnaires were administered face-to-face to the three categories of respondents (radiographers, radiology assistants, and patients) who meet the specific set of inclusion criteria, following a brief explanation about the research aim. Consent was gotten by way of a signed consent form and ethical approval obtained. A Likert 5-point scale was utilized in analyzing the responses, undergoing descriptive statistics using SPSS (version 25) software. Results QMS is extremely useful in workflow, accuracy, communication, combatting work stress, and maintaining privacy, but with accompanying occasional technical challenges. A remarkable preference for QMS to manual in CXR-TB screening was noted among all research subjects, with strong level of agreement (close mean values of 4.06, 3.81, 3.91; standard deviation of 0.70, 0.73, 0.60). Conclusion Findings from this study uncover the vital role the QMS plays in improving the quality of CXR-TB screening services, demonstrating great acceptability.

The Low Extra Delay Background Transport (LED-BAT) protocol is a recently standardized protocol that aims to offer a scavenger service (i.e. the goal is to exploit the remaining and unused capacity of a link). LEDBAT is a delay-based protocol mainly defined by two parameters: a target queuing delay and a gain. The RFC 6817 provides guidelines to configure both parameters that strongly impact on the LEDBAT behavior in terms of fairness with other protocols. However, these guidelines are questioned by several studies as they might lead to the generation of a non-LBE (Less-than-Best-Effort) traffic. This paper explores the set of optimal parameters allowing LEDBAT protocol to effectively perform as an LBE traffic. We conclude that the optimal couple of target and decrease gain is (5 ms; 10). However, we observe that the aggregated use of optimized LEDBAT sources still disturb the overall traffic performance and that the exponential backoff is not an answer to this issue. As a result, we believe that additional strategies to limit the number of LEDBAT flows are required for integrating this protocol at a large scale.

Delay-based congestion control algorithms provide higher throughput and stability than traditional loss-based AIMD algorithms, but they are inherently unfair against older connections when the queuing and the propagation delay cannot be measured accurately and independently. This paper presents a novel measurement algorithm whereby fairness between old and new connections is preserved. The algorithm does not modify the dynamics of congestion control, and runs entirely in the server host using locally available information.

We consider the problem of simultaneous scheduling and resource allocation of an incoming flow of requests to a set of computing units. By representing each computing unit as a node, we model the overall system as a multiqueue scheme. Inspired by congestion control approaches in communication networks, we propose an AIMD-like (additive increase multiplicative decrease) admission control policy that is stable irrespective of the total number of nodes and AIMD parameters. The admission policy allows us to establish an event-driven discrete model, triggered by a locally identifiable enabling condition. Subsequently, we propose a decentralized resource allocation strategy via a simple nonlinear state feedback controller, guaranteeing global convergence to a bounded set in finite time. Last, we reveal the connection of these properties with Quality of Service specifications, by calculating local queuing time via a simple formula consistent with Little's Law.

Dynamic queueing networks (DQN) model queueing systems where demand varies strongly with time, such as airport terminals. With rapidly rising global air passenger traffic placing increasing pressure on airport terminals, efficient allocation of resources is more important than ever. Parameter inference and quantification of uncertainty are key challenges for developing decision support tools. The DQN likelihood function is, in general, intractable and current approaches to simulation make likelihood-free parameter inference methods, such as approximate Bayesian computation (ABC), infeasible since simulating from these models is computationally expensive. By leveraging a recent advance in computationally efficient queueing simulation, we develop the first parameter inference approach for DQNs. We demonstrate our approach with data of passenger flows in a real airport terminal, and we show that our model accurately recreates the behaviour of the system and is useful for decision support. Special care must be taken in developing the distance for ABC since any useful output must vary with time. We use maximum mean discrepancy, a metric on probability measures, as the distance function for ABC. Prediction intervals of performance measures for decision support tools are easily constructed using draws from posterior samples, which we demonstrate with a scenario of a delayed flight.

In asymptotic regimes, both in time and space (network size), the derivation of network capacity results is grossly simplified by brushing aside queueing behavior in non-Jackson networks. This simplifying double-limit model, however, lends itself to conservative numerical results in finite regimes. To properly account for queueing behavior beyond a simple calculus based on average rates, we advocate a system theoretic methodology for the capacity problem in finite time and space regimes. This methodology also accounts for spatial correlations arising in networks with CSMA/CA scheduling and it delivers rigorous closed-form capacity results in terms of probability distributions. Unlike numerous existing asymptotic results, subject to anecdotal practical concerns, our transient results can be used in practical settings, e.g., to compute the time scales at which multi-hop routing is more advantageous than single-hop routing.

This paper considers the distribution of a general peak age of information (AoI) model and develops a general analysis approach for probabilistic performance guarantee from the time-domain perspective. Firstly, a general relationship between the peak AoI and the inter-arrival and service times of packets is revealed. With the help of martingale theory, a probabilistic bound on the peak AoI is then derived for the general case of endogenous independently and identically distributed increments in information generation and transmission processes. Thereafter, the application of the obtained bound is illustrated with the M/M/1 and D/M/1 queuing models. The validity of the proposed bound is finally examined with numerical results.

To meet the growth of real-time and multimedia traffic, the next generation of satellite networks with a guarantee of quality of service (QoS) is indeed, urgent. In this paper, we support the multi-layered satellite network as the scenario, owing to dynamic topology and distinct classification of the generated traffics. We map the satellite network system into a tandem queuing model, which the purpose is devoted to use a mathematical tool for evaluating the performance bounds of per-flow end-to-end networks. For delay-sensitive traffics, we compare two different arrival models-Poisson process and self-similar process. Meanwhile, we apply traditional scheduling strategy to MEO nodes while considering link impairment between a pair of satellites. Finally, we analyze, in a numerically way, which parameters (and how they) influence the perflow end-to-end performance bounds. Our analysis can be used as a reference to China's future satellite topology and routing algorithms designed and, optimization given a network with performance requirements and constraints.

Length Rate Quotient (LRQ) is the first algorithm of interleaved shaping -a novel concept proposed to provide per-flow shaping for a flow aggregate without per-flow queuing. This concept has been adopted by Time-Sensitive Networking (TSN) and Deterministic Networking (DetNet). An appealing property of interleaved shaping is that, when an interleaved shaper is appended to a FIFO system, it does not increase the worst-case delay of the system. Based on this "shaping-for-free" property, an approach has been introduced to deliver bounded end-to-end latency. Specifically, at each output link of a node, class-based aggregate scheduling is used together with one interleaved shaper per-input link and per-class, and the interleaved shaper re-shapes every flow to its initial traffic constraint. In this paper, we investigate other properties of interleaved LRQ shapers, particularly as stand-alone elements. In addition, under per-flow setting, we also investigate per-flow LRQ based flow aggregation and derive its properties. The analysis focuses directly on the timing of operations, such as shaping and scheduling, in the network. This timing based method can be found in the Guaranteed Rate (GR) server model and more generally the max-plus branch of network calculus. With the derived properties, we not only show that an improved end-to-end latency bound can be obtained for the current approach, but also demonstrate with two examples that new approaches may be devised. End-to-end delay bounds for the three approaches are derived and compared. As a highlight, the two new approaches do not require different node architectures in allocating (shaping / scheduling) queues, which implies that they can be readily adapted for use in TSN and DetNet. This together with the derived properties of LRQ shed new insights on providing the TSN / DetNet qualities of service.

Multiclass FIFO is used in communication networks such as in input-queueing routers/switches and in wireless networks. For the concern of providing service guarantees in such networks, it is crucial to have analytical results, e.g. bounds, on the performance of multi-class FIFO. Surprisingly, there are few such results in the literature. This paper is devoted to filling the gap. Specifically, a single hop deterministic case is studied, for which, delay and backlog bounds are derived, in addition to guaranteed rate and service curve characterizations that may be exploited to extend the analysis to network cases.

High-intensity concurrent arrivals of request packets in Internet traffic can cause dependence of event-to-event-times of the requests being served, which causes non-memoryless, modelled with heavy-tail distributions unlike common known traffics. The performance of Internet traffic can be examined using analytical models for the purpose of optimizing the system to reduce its operating costs. Therefore, our study examined a Ga/M/1/K Internet queue class (Gamma arrival processes, Ga; with memoryless-Poisson service process, M; a single server, 1, and K waiting room) and proposed specific derivations of its performance indicators. Real-life data of a corporate organisation Internet server was monitored at both peak and off-peak periods of its usage for Internet traffic data analysis. The minimum ‘0’ in the arrival process indicates self-similarity and was assessed using Hurst parameter, H, and their (standard deviation). ‘H’ > 0.5 arrival process in the peak period only, indicates s...

We present a search and rescue problem as a final project for an undergraduate-level Introduction to Robotics course. To successfully complete the project, a participating robot has to solve four sub-problems that are currently among the most actively researched areas in robotics: computer vision, manipulative robotics, localization, and multi-robot cooperation. By immersing the students in the details of these sub-problems, we aim to have them develop a deeper appreciation of the difficulties. In many cases, this experience also motivates the students to pursue research in those areas. We describe several example systems that use easily obtained hardware components such as LEGO pieces, the Handyboard, sonar, compass, CMUCam, and servomotors. However, each of the sub-problems is easily extendable to increase the complexity/creativity of the solution as well as accommodate for new and more powerful devices.

This paper briefly discusses the various attendance monitoring technologies from manual to automated monitoring systems. Also, the Authors discussed on the impacts through strengthening the key features in contributing a more timely and efficient performance of employees, students and other external parties. Extended research of evolving attendance systems will be discussed further.

The legal system in Nigeria is be-deviled with delayed justice which has become a source of concern to many person. This is very much peculiar to those who feel that the judiciary is too slow in resolving legal issues in Nigeria. In Nigeria, there abound court cases especially those of criminal dimensions that have ongoing for years now without reaching a conclusive conclusion. The study is aimed at modelling the queuing system in the magistrate courts in Onitsha Magisterial districts. The specific objectives include: to apply the M/M/2 and M/M/3 models with identical and parallel queues to criminal cases in the Magistrate court and to compare the efficiency of the two models and in either cases to determine time to justice in criminal cases in the Magisterial District. The results of the study show that M/M/2 model with 2 identical and parallel queues have an expected number of cases in the system as 39 with 50% idle time while the M/M/3 model with 3 identical and parallel queues have an expected number of cases in the system as 23 cases with 64.88% idle time. The comparison of the two models shows M/M/2 with 2-identical and parallel queues is more efficient as it has more number of cases to attend to and less idle time. The study therefore concludes that the delays in the disposal of cases especially those with criminal nature may not be attributable to the queuing systems in place. Even though lesser number of servers is seen to be efficient, this may not be advised. Increasing the number of servers though will increase speed of disposal of cases, may also lead to increased idle time of servers. As more courts being set up may result in waste of resources, manpower and time as the 2-server system is efficient in speeding up justice delivery in the magisterial division.

This paper studies the effects of tuning delay of transmitters in packet-based optical broadcast networks. We consider scheduling of random traffic with tunable transmitters and fixed-tuned receivers and obtain the degradation imposed by tuning delay using several performance criteria, such as schedule completion time, average packet delay, and session blocking rates. We show that for off-line scheduling the effects of tuning delay are small even if the tuning time is as large as the packet duration. We provide a lower bound to the expected completion time of any off-line schedule with an arbitrary number of wavelengths. We then describe a near-optimal schedule which is based on the principle of having idle transmitters tune to wavelengths just-in-time to start their transmissions. Stability and capacity issues in the transmission of real-time traffic are considered and a queueing-theoretic analysis of average packet delay is given. Packet delay is found to he insensitive to tuning delay under nearoptimal transmission scheduling. Finally we extend the model to connection-oriented networks and evaluate the session blocking performance for scheduled circuit connections.

This letter considers a problem that arises in the context of statistical, state-dependent resource allocation in communication networks. Specifically, the problem concerns a single-server discrete-time queue with state-dependent probabilistic server interruptions. The system is analyzed for two forms of probabilistic behavior: exponential and hyperbolic forms. The analysis yields several performance metrics of interest, including average system occupancy, average delay, steady-state occupancy distribution.

This paper prcseirts aj'2edback contrd design for isolated ramp metering cmtrol. This feedback control design, i:nlike the existing isolated feedback ramp controllers, Glso ta1:es into account (he ramp queue length. Using a !ionlizmr Hm ;ontrol design methodology, we formulate ihe problem in the desired setting to be able to utilize the results of the methodolop.

This paper presents a mathematical framework for dynamic congestion pricing. The objective is to calculate an optimal toll using the optimal control theory. The problem consists of tolled lanes or routes and alternate non-tolled lanes or routes. The model is developed using a traffic conservation law, the queuing theory, and fundamental macroscopic relationships. A logit model is used for establishing the relationship between the price and the driver's choice behavior. We design a cost function and then use Hamilton-Jacobi-Bellman equation to derive an optimal control law that uses real-time information to determine an optimal tolling price. Simulations are performed to demonstrate the performance of this optimal control congestion-pricing algorithm.

This paper presents a mathematical model for dynamic congestion pricing at a toll where alternate lane or routes are available. The model developed is based on traffic conservation law and queueing, and moreover uses fundamental macroscopic relationships for its derivation. The modeling uses a Logit model for the price and driver choice behavior relationship. We use this nominal mathematical model for the dynamics to derive a feedback control law that uses real-time information to come up with tolling price. Simulation results show the performance of this dynamic feedback congestion pricing algorithm.

Queueing models provide a useful tool for predicting the performance of many service systems including computer systems, telecommunication systems, computer/communication networks and flexible manufacturing systems. Traditional queueing models predict system performance under the assumption that all service facilities provide failure-free service. It must, however, be acknowledged that service facilities do experience faiiures and that they get repaired. In recent years, it has been increasingly recognized that this separation of performance and reliability/availability models is no longer adequate.

Previous covering models for emergency service consider all the calls to be of the same importance and impose the same waiting time constraints independently of the service's priority. This type of constraint is clearly inappropriate in many contexts. For example, in urban medical emergency services, calls that involve danger to human life deserve higher priority over calls for more routine incidents. A realistic model in such a context should allow prioritizing the calls for service. In this paper a covering model which considers different priority levels is formulated and solved. The model heritages its formulation from previous research on Maximum Coverage Models and incorporates results from Queuing Theory, in particular Priority Queuing. The additional complexity incorporated in the model justifies the use of a heuristic procedure.

There have been many queuing analyses for a single server queue fed by an M/G/∞ traffic process, in which G is a Pareto Distribution, that focus on certain limiting conditions. In this paper we enhance the so-called Quasi-Stationary (QS) approximation -a queuing analysis introduced previously that provides an algorithm for computation of an accurate approximation for the stationary queue distribution, applicable to the entire range of system parameters. By numerical evaluation of the QS approximation and the asymptotic approximations (large buffer, many sources, and heavy traffic) over an extremely wide range of parameter values we are able to graphically display consistency of the QS approximation with all the asymptotic results. We demonstrate that the accuracy of the asymptotic approximations is satisfactory only in limited regions of the system parameter space.

This paper exploits classical control theory to design congestion control algorithms for "best effort" traffic in ATM networks. The control goal is the full utilisation of network links without incurring cell losses. A fluid model approximation of cell flows is assumed and linear differential equations are used to model the dynamics of network queues in response to ABR traffic and quality constrained (CBR+ VBR) traffic. The available ABR bandwidth is modelled by means of an unknown and bounded disturbance function. A general end to end control algorithm that feeds back to the source the space that is free in the network buffers is included in the model and a particular one is proposed which is based on Smith's principle. The linearity and the simplicity of the proposed control law allow us to prove, via mathematical analysis, that the algorithm always guarantees no cell losses whereas full utilisation of network links is ensured if the capacity of per-VC buffers is at least equal to the VC bandwidth-delay product. Moreover, per-VC queuing easily allows switches to enforce fairness. Finally, it is shown how performance evaluation can be easily carried out using SIMULINK for MATLAB, which is a software tool widely used by control engineers to simulate dynamic systems. In this way, the effort to develop discrete event simulations is saved.

We model the hospital as seeking to balance the costs to itself in providing care, as well as the societal cost of people waiting for care. We use queuing theory to show that the optimal capacity and the corresponding optimal occupancy rate are dependent on the marginal cost of expanding capacity, the marginal cost of waiting, and the rates of patient arrival and discharge. Therefore, a universal occupancy target is unfounded. As well, the model shows that increasing capacity to respond to increased patient influxes is inadequate, suggesting that the healthcare system must explore alternate responses to burgeoning patient populations.

Queues are not merely an object to study. Queues are real world problems faced by customers at a busi- ness station that kill their valuable time. This results in decreased customer interest and the progress trends towards a loss. This is particularly frightful with smaller investments, where a single loss may permanently eliminate the business. It is not enough to know how queue behaves, but we are also required to know how to eliminate queues or at least how to reduce them to a manageable size. It is possible to reduce the queuing delay by changing the service mechanism. This involves increasing the rate at which customers are being served. Queues grow when customers happen to arrive at a faster rate than they are being served. This type of service dependent queues may be eliminated or at least reduced by developing a demand responsive service strategy that reduces the service time variation. Practical business transactions are too complex to be studied analytically. Besides, anal...

The relationship between setup time reduction and performance improvement in the stochastic closed manufacturing cell is addressed. The improved cell performance is linked with the potential competitive advantage of the firm in the marketplace. An M/G/1 queueing model of a 'closed manufacturing cell' (i.e., the cell produces to stock rather than to order) is formulated. Decreasing marginal improvements in cell flow time are shown to result from job setup time reductions. Additionally, marginal reductions in optimal product batch sizes and flow time variance are also shown to diminish as job setup time decreases. Suggestions are provided for allocating limited capital among heterogeneous products for setup time reduction purposes. For a given product mix, optimal allocation of setup time reduction investment is shown to be dependent on key product and production parameters.

This study aims to determine the Single Channel -Single Phase Teller queuing system at PT. Bank BJB KCP Gedebage Bandung. Where there is a decrease in the percentage of queue visits in 2023 by 14.21%. Descriptive Qualitative Method by collecting data on the number of customer queue visits processed by the author, namely in the form of data on the number of customer queue visits in 2023 from January to December. The results showed that PT. Bank BJB KCP Gedebage has a queuing system machine called BJB SANTER (Integrated Customer Analysis System) which is carried out offline with features or services on the frontliner. BJB SANTER is done to pull data by Regional Office to monitor Teller performance, to ensure customer satisfaction. The author's suggestion is that PT. Bank BJB KCP Gedebage Bandung can implement a Multi Channel -Single Phase queuing system so that customers can be served simultaneously by several tellers, and can apply the BJB SANTER system can be accessed online via smartphone. So that it will be able to increase the number of customers, especially at PT. Bank BJB KCP Gedebage Bandung.

This paper develops an improved analysis of ATM switching architectures adopting a replicated banyan interconnection network provided with dedicated input and output queues, one per switch inlet and outlet. Two different plane selection policies are studied, random choice and alternate sharing, and two different operation modes are considered for the interaction between input and output queues, backpressure and output queue loss. These different internal operations are ranked in terms of traffic performance and the problem of optimal allocation of a given buffer budget between input and output queues is addressed. The analysis, which assumes that the network is loaded by uniform traffic, always provides conservative results whereas known models are less accurate and give optimistic traffic results. Packet delay and loss probability performance is evaluated for the ATM switch and its accuracy is assessed using computer simulation also in comparison with results given by previous models.

Hazard rates play an important role in various areas, e.g., reliability theory, survival analysis, biostatistics, queueing theory and actuarial studies. Mixtures of distributions are also of a great preeminence in such areas as most populations of components are indeed heterogeneous. In this study we present a sufficient condition for mixtures of two elements of the same natural exponential family (NEF) to have an increasing hazard rate. We then apply this condition to some classical NEF's having either quadratic, or cubic variance functions (VF) and others as well. A particular attention is devoted to the hyperbolic cosine NEF having a quadratic VF, the Ressel NEF having a cubic VF and to the Kummer distributions of type 2 NEF. The application of such a sufficient condition is quite intricate and cumbersome, in particular when applied to the latter three NEF's. Various lemmas and propositions are needed then to verify this condition for these NEF's.