Stationary Performance Measures Research Articles

Transient Analysis for a Queuing System with Impatient Customers and Its Applications to the Pricing Strategy of a Video Website

In this paper, we consider a queuing system with impatient customers, which includes infinite servers and two types of customers. During the service process, Type-1 customers may leave the system or upgrade to be Type-2 customers due to their impatience. By solving the partial differential equations, we obtain the generating functions of the transient distribution of the queue length, and many stationary performance measures are further derived. Then, as an application, we formulate an expected profit function for a video website, and maximize it by determining the optimal pricing strategy. Finally, numerical examples are provided to demonstrate the impacts of parameters on the optimal website profit.

Performance characteristics of the fork-join queuing system

Objectives. The problem of investigating a fork-join queuing system is considered. It is required to build the process of the system functioning, to find the condition for the existence of a stationary distribution, and propose algorithms for calculating the stationary distribution and the main stationary performance characteristics. The special interest of the study is to obtain the lower and upper bounds of the mean sojourn time of a customer in the system.Methods. Methods of probability theory, queuing theory and matrix theory are used.Results. The functioning of the system is described in terms of a multidimensional Markov chain. A constructive condition for the existence of a stationary distribution is found, and algorithms for calculating the stationary distribution and stationary performance characteristics of the system are proposed. Analytical expressions are obtained for the lower and upper bounds of the mean sojourn time of customers in the system.Conclusion. The functioning of the fork-join queuing system with a stationary Poisson flow has been studied. Each of the arriving customers forks into two tasks that go to two subsystems, each of which consists of a server and a buffer. We assume that the buffer to one of the servers is unlimited, and to the second server has a finite volume. Service times have, generally speaking, different phase distributions (PH-Phase type distributions). For this system, a condition for the existence of a stationary distribution is obtained, algorithms for calculating the stationary distribution and a number of stationary performance measures of the system are proposed. Analytical expressions for the lower and upper bounds of the mean sojourn time of a customer in the system from the moment it enters the system to the moment of synchronization, which is a critical performance indicator of the fork-join queues, are obtained. The results of the study can be used for modeling various computer and communication systems, in particular, systems that perform parallel computing, customer processing in distributed databases, and parallel disk access.

Stationary analyses for a double-ended queueing system with random service capacity and balking customers

Stationary analyses for a double-ended queueing system with random service capacity and balking customers

A Study of Congestion-Based Information Guidance Policy for Hierarchical Healthcare Systems

This paper develops a queueing system model to analyze the operations of a hierarchical healthcare system consisting of general hospitals (GHs) and community healthcare centers (CHCs). GHs typically provide a higher level of health care service than CHCs, and thus are preferred choices for many patients’ healthcare service needs. Consequently, GHs are often heavily congested and patients often incur excessive waiting time. In contrast, CHCs are often idle and resources are underutilized. To help balance the utilization of resources in GHs and CHCs, a congestion-based information guidance policy is proposed in this paper to inform patients in the GH service queue about the anticipated delay. Upon being informed the delay for GH service, patients may balk, remain in queue for GH service, or switch to receive service at CHCs. This policy is thus expected to relieve the congestion at GHs and promote CHC usage. To study the effects of the proposed policy, a hierarchical healthcare system is modeled as a queueing system with strategic patients. Stationary performance measures of the system are analytically characterized using a Markov chain model. Stochastic and numerical analyses provide insights on how to design information guidance policy that would help improve overall health care service quality under different scenarios.

Methodology to Predict Federal Performance Measures From State Performance Measures of Pavement Networks

Pavement management data used in measuring the performance of a pavement network contribute to managing maintenance and rehabilitation needs and determining the required funding levels. A network’s performance can be measured in several ways. The method adopted by the Virginia Department of Transportation has been in use for more than 15 years. With the introduction of Transportation Performance Management by the Federal Highway Administration (FHWA), a set of performance measures required by FHWA are to be reported. A few methods from earlier efforts by others in predicting one or more pavement performance parameters are briefly discussed. The main challenges in the determination of federal performance measures are the lack of prediction models for those measures; the reporting on 1/10th-mi sections that are not directly used in analysis and maintenance planning; and the determination of funding levels based on 1/10th-mi sections. In this paper, a new method to predict the federal performance measures of pavement networks from the state performance measures is provided, along with the mathematical models developed.

Measuring performance: Ranking state success over two decades in India

This paper proposes new composite measures of relative and dynamic state performance to improve governance and delivery of public programs in developing countries with a federal structure. We illustrate the use of the indices to rank the performance of 19 major Indian states on two large development programs launched by the Indian government over the last two decades using publicly available data. Although we find volatility in performance over time, there exists a positive correlation between measures of initial (administrative) state capacity, development and accountability with program outcomes. Our findings have important implications for both the design and implementation of large-scale public programs across developing countries.

Joint replacement and production control for a queueing system with different failures

ABSTRACT We propose a new integrated queueing-inventory and reliability model. First, we obtained time-dependent performance measures by using the Laplace transform method. Then, we derived stationary performance measures by using alternative solution methods, including the probability generating function and matrix geometric method. Optimization procedures were developed for both make-to-order and make-to-stock cases. Performance evaluation of the derived time-dependent and stationary performance measures were reviewed first. Then we compared joint replacement and production-inventory control with separate optimization for respective production modes. Finally, the impact of deteriorated services under different demand rates and parameter settings was investigated. Prior studies are neglecting the mutual interaction between production and reliability. This study contributes to filling the gap. In our proposed numerical example, a cost reduction of more than one-third was achieved by joint optimization. The result shows that decision-maker should make his decisions in an integrated manner otherwise the price paid may be significant.

Modeling of Interconnected Infrastructures with Unified Interface Design toward Smart Cities

In recent years, there have been tendencies to enable smart cities with interconnected infrastructures and communities. Current engineering design and operation practices are limited to handling individual systems with modeling and simulation, as well as control systems. This paper presents a holistic approach with engineering practice to design and operate interconnected systems as part of smart cities. The approach is based on modeling individual physical systems and associated processes and identifying key performance indicators to evaluate each system and interconnected systems with an understanding of the coupling among systems to increase the overall performance of interconnected systems. The multi-objective optimization technique is proposed to achieve the best performance based on system design, control, and operation parameters. Due to the multidimensional nature of the interconnected systems, a unified interface system with modular design is proposed to achieve the highest overall performance of the interconnected systems with standardized interactions among state variables and performance measures. The proposed approach can allow dynamic updates of the interconnected systems based on model libraries of each system and process. A case study is presented of interconnected energy–water–transportation–waste facilities, whereby modeling is discussed, and performance measures are evaluated for different scenarios using the unified interface design.

Sensitivity Analysis for the Stationary Distribution of Reflected Brownian Motion in a Convex Polyhedral Cone

Reflected Brownian motion (RBM) in a convex polyhedral cone arises in a variety of applications ranging from the theory of stochastic networks to mathematical finance, and under general stability conditions, it has a unique stationary distribution. In such applications, to implement a stochastic optimization algorithm or quantify robustness of a model, it is useful to characterize the dependence of stationary performance measures on model parameters. In this paper, we characterize parametric sensitivities of the stationary distribution of an RBM in a simple convex polyhedral cone, that is, sensitivities to perturbations of the parameters that define the RBM—namely the covariance matrix, drift vector, and directions of reflection along the boundary of the polyhedral cone. In order to characterize these sensitivities, we study the long-time behavior of the joint process consisting of an RBM along with its so-called derivative process, which characterizes pathwise derivatives of RBMs on finite time intervals. We show that the joint process is positive recurrent and has a unique stationary distribution and that parametric sensitivities of the stationary distribution of an RBM can be expressed in terms of the stationary distribution of the joint process. This can be thought of as establishing an interchange of the differential operator and the limit in time. The analysis of ergodicity of the joint process is significantly more complicated than that of the RBM because of its degeneracy and the fact that the derivative process exhibits jumps that are modulated by the RBM. The proofs of our results rely on path properties of coupled RBMs and contraction properties related to the geometry of the polyhedral cone and directions of reflection along the boundary. Our results are potentially useful for developing efficient numerical algorithms for computing sensitivities of functionals of stationary RBMs.

Measuring Performance: Ranking State Success Over Two Decades in India

This paper proposes new composite measures of relative and dynamic state performance to improve governance and delivery of public programs in developing countries with a federal structure. We rank the performance of 19 major Indian states on two large development programs launched by the Indian government over the last two decades using publicly available data. Although we find volatility in performance over time, there exists a positive correlation between measures of state capacity, development and accountability with program outcomes. Our findings have important implications for both the design and implementation of public service programs of such large scale.

Analysis of an M/PH/1 Retrial Queueing-Inventory System with Level Dependent Retrial Rate

We analyze a queueing-inventory system which can model airline and railway reservation systems. An arriving customer to an idle server joins for service immediately with exactly one item from inventory at the moment of service completion if there are some on-hand inventory, or else he accesses to a buffer of varying size (the buffer capacity varies and equals to the number of the items in the inventory with maximum size S). When the buffer overflows, the customer joins an orbit of infinite capacity with probability p or is lost forever with probability 1−p. Arrivals form a Poisson process, and service time has phase type distribution. The time between any two successive retrials of the orbiting customer is exponentially distributed with parameter depending on the number of customers in the orbit. In addition, the items have a common life time with exponentially distributed. Cancellation of orders is possible before their expiry and intercancellation times are assumed to be exponentially distributed. The stability condition and steady-state probability vector have been studied by Neuts–Rao truncation method using the theory of Level Dependent Quasi-Birth-Death (LDQBD) processes. Several stationary performance measures are also computed. Furthermore, we provide numerical illustration of the system performance with variation in values of underlying parameters and analyze an optimization problem.

Queuing System with Two Types of Customers and Dynamic Change of a Priority

The use of priorities allows us to improve the quality of service of inhomogeneous customers in telecommunication networks, inventory and health-care systems. An important modern direction of research is to analyze systems in which priority of a customer can be changed during his/her stay in the system. We considered a single-server queuing system with a finite buffer, where two types of customers arrive according to a batch marked Markov arrival process. Type 1 customers have non-preemptive priority over type 2 customers. Low priority customers are able to receive high priority after the random amount of time. For each non-priority customer accepted into the buffer, a timer, which counts a random time having a phase type distribution, is switched-on. When the timer expires, the customer with some probability leaves the system unserved and with the complimentary probability gains the high priority. Such a type of queues is typical in many health-care systems, contact centers, perishable inventory, etc. We describe the behavior of the system by a multi-dimensional continuous-time Markov chain and calculate a number of the stationary performance measures of the system including the various loss probabilities as well as the distribution function of the waiting time of priority customers. The illustrative numerical examples giving insights into the system behavior are presented.

Markov processes in blockchain systems

In this paper, we develop a more general framework of block-structured Markov processes in the queueing study of blockchain systems, which can provide analysis both for the stationary performance measures and for the sojourn time of any transaction or block. In addition, an original aim of this paper is to generalize the two-stage batch-service queueing model studied in Li et al. (Blockchain queue theory. In: International conference on computational social networks. Springer: New York; 2018. p. 25–40) both “from exponential to phase-type” service times and “from Poisson to MAP” transaction arrivals. Note that the MAP transaction arrivals and the two stages of PH service times make our blockchain queue more suitable to various practical conditions of blockchain systems with crucial factors, for example, the mining processes, the block generations, the blockchain building and so forth. For such a more general blockchain queueing model, we focus on two basic research aspects: (1) using the matrix-geometric solution, we first obtain a sufficient stable condition of the blockchain system. Then, we provide simple expressions for the average stationary number of transactions in the queueing waiting room and the average stationary number of transactions in the block. (2) However, on comparing with Li et al. (2018), analysis of the transaction–confirmation time becomes very difficult and challenging due to the complicated blockchain structure. To overcome the difficulties, we develop a computational technique of the first passage times by means of both the PH distributions of infinite sizes and the RG factorizations. Finally, we hope that the methodology and results given in this paper will open a new avenue to queueing analysis of more general blockchain systems in practice and can motivate a series of promising future research on development of blockchain technologies.

Examining positive body image, sport confidence, flow state, and subjective performance among student athletes and non-athletes

The primary purpose of the present study was to examine differences in positive body image, specifically body appreciation and functionality appreciation, between student athletes and non-athletes. A secondary purpose was to examine the relationships between positive body image and other sport-related variables. Seventy-nine National Collegiate Athletic Association (NCAA) Division I student athletes (Mage = 19.79, SD = 1.13) and 175 non-athletes (Mage = 19.38, SD = 1.81) completed measures of body appreciation and functionality appreciation. The athletes further completed measures of sport confidence, flow state, and subjective sport performance. Student athletes reported higher levels of both facets of positive body image. Significant relationships were also found between positive body image and the sport-related variables. The present results contribute novel findings to the positive body image literature and potential implications for coaches to encourage a culture that focuses less on body appearance and more on cultivating positive body image.

A continuous review (<i>s</i>, <i>S</i>) inventory system with postponed demands at service facility

In this article, we present a continuous review (s, S) inventory system with a service facility consisting of finite waiting hall (capacity N) and a single server. The customers arrive according to a Poisson process. The individual customer's unit demand is satisfied after a random time of service, which is assumed to be exponential. An arriving customer, who finds the waiting hall is full, enters into the pool of infinite size or leaves the system which is according to a Bernolli trial. The joint probability distribution of the number of customers in the pool, number of customers in the waiting hall and the inventory level is obtained in the steady-state case. Various stationary system performance measures are computed and total expected cost rate is calculated. The results are illustrated numerically. [Received: 8 January 2017; Revised: 28 February 2018; Accepted: 30 July 2018]

Title V Maternal and Child Health Services Block Grant Priority Needs and Linked Performance Measures: Current Patterns and Trends (2000-2015).

Objective As part of the Title V Maternal and Child Health (MCH) Services Block Grant, administered by the Health Resources and Services Administration's (HRSA's) Maternal and Child Health Bureau (MCHB), states are required to conduct a comprehensive needs assessment identifying MCH priorities every 5years. The most current needs assessment (2015) occurred after a transformation of the program, in which a new performance measurement framework was created. This analysis examined current patterns and trends in state MCH priorities and selected performance measures to identify changing needs and inform technical support. Methods Multiple coders categorized: (1) state priority needs from 2000 to 2015 into focus areas and subcategories for examination of current, diminishing, and emerging needs; and (2) the selection of linked national and state performance measures in 2015 for all 59 states and jurisdictions. Results Between 2000 and 2015, the proportion of states with a need around pre- and inter-conception care increased from 19% to 66%. More states had needs in the breastfeeding subcategory (42%) compared with 20% of states or less in previous years. Fewer states had needs around data capacity than in past years. Emerging needs included supporting families/relationships. The most commonly selected national performance measures (NPMs) were around breastfeeding and well-woman visits. The state performance measures (SPMs) analysis also emphasized assets, with measures around community/context and positive development. Teen births and postpartum depression were areas where multiple states had SPMs. Conclusions for practice Increasing and emerging needs may help to inform technical assistance and future national measures for the Title V program.

Analysis of a batch service multi-server polling system with dynamic service control

This paper considers a multi-server polling system with batch service of an unlimited size, i.e., the so called 'Israeli queue' with multi-server, where the service rate of each server switches between a low and a high value depending on the number of groups standing in front of the servers upon its service completion. By means of matrix geometric method and LU-type RG factorization of the infinitesimal generator in irreducible QBD process, the explicit closed-form of rate matrix $R$ and the steady state distribution of the queue length are respectively derived. In terms of the results, some stationary performance measures are obtained. In addition, some numerical examples are presented.

Successful Incorporation of Performance Based Payments for Trauma Center Readiness Costs into the Georgia Trauma System

As quality and outcomes have moved to the fore front of medicine in this era of healthcare reform, a state trauma system Performance Based Payments (PBP) program has been incorporated into trauma center readiness funding. The purpose of this study was to evaluate the impact of a PBP on trauma center revenue. From 2010 to 2016, a percentage of readiness costs funding to trauma centers was placed in a PBP and withheld until the PBP criteria were completed. To introduce the concept, only three performance criteria and 10 per cent of readiness costs funding were tied to PBP in 2010. The PBP has evolved over the last several years to now include specific criteria by level of designation with an increase to 50 per cent of readiness costs funding being tied to PBP criteria. Final PBP distribution to trauma centers was based on the number of performance criteria completed. During 2016, the PBP criteria for Level I and II trauma centers included participation in official state meetings/conference calls, required attendance to American College of Surgeons state chapter meetings, Trauma Quality Improvement Program, registry reports, and surgeon participation in Peer Review Committee and trauma alert response times. Over the seven-year study period, $36,261,469 was available for readiness funds with $11,534,512 eligible for the PBP. Only $636,383 (6%) was withheld from trauma centers. A performance-based program was successfully incorporated into trauma center readiness funding, supporting state performance measures without adversely affecting the trauma center revenue. Future PBP criteria may be aligned to designation standards and clinical quality performance metrics.

M/g/c/c State Dependent Queueing Model for Road Traffic Simulation

In this paper, we present a stochastic queuing model for the road traffic, which captures the stationary density-flow relationships in both uncongested and congestion conditions. The proposed model is based on the $M/g/c/c$ state dependent queuing model of Jain and Smith, and is inspired from the deterministic Godunov scheme for the road traffic simulation. We first propose a reformulation of the $M/g/c/c$ state dependent model that works with density-flow fundamental diagrams rather than density-speed relationships. We then extend this model in order to consider upstream traffic demand as well as downstream traffic supply. Finally, we calculate the speed and travel time distributions for the $M/g/c/c$ state dependent queuing model and for the proposed model, and derive stationary performance measures (expected number of cars, blocking probability, expected travel time, and throughput). A comparison with results predicted by the $M/g/c/c$ state dependent queuing model shows that the proposed model correctly represents the dynamics of traffic and gives good performances measures. The results illustrate the good accuracy of the proposed model.

Interval optimality analysis in Erlang bulk arrival model in fuzzy environment

In this paper, we propose a methodology to analyse the best arrival of K-phase Erlang distribution in fuzzy environment. We consider the queue parameters as triangular fuzzy numbers. At first, we construct the inverse membership of the steady state performance measures. Second, we construct the pairs of MINLP to calculate the lower and upper bound of the performance measure at the different possibility level of α via Zadeh extension principle. We analyse the interval of the best arrival optimality using testing of hypothesis. A numerical example is illustrated.