This paper studies an M/M/1 retrial queue with negative customers, passive breakdown, and delayed repairs. Assume that the breakdown behavior of the server during idle periods is different from that during busy periods. Passive breakdowns may occur when the server is idle, due to the lack of monitoring of the server during idle periods. When the passive breakdown occurs, the server does not get repaired immediately and enters a delayed repair phase. Negative customers arrive during the busy period, which will cause the server to break down and remove the serving customers. Under steady-state conditions, we obtain explicit expressions of the probability generating functions for the steady-state distribution, together with some important performance measures for the system. In addition, we present some numerical examples to illustrate the effects of some system parameters on important performance measures and the cost function. Finally, based on the reward-cost structure, we discuss Nash equilibrium and socially optimal strategy and numerically analyze the influence of system parameters on optimal strategies and optimal social benefits.

Cloud storage faces many problems in the storage process which badly affect the system's efficiency. One of the most problems is insufficient buffer space in cloud storage. This means that the packets of data wait to have storage service which may lead to weakness in performance evaluation of the system. The storage process is considered a stochastic process in which we can determine the probability distribution of the buffer occupancy and the buffer content and predict the performance behavior of the system at any time. This paper modulates a cloud storage facility as a fluid queue controlled by Markovian queue. This queue has infinite buffer capacity which determined by the M/M/1/N queue with constant arrival and service rates. We obtain the analytical solution of the distribution of the buffer occupancy. Moreover, several performance measures and numerical results are given which illustrate the effectiveness of the proposed model.

A recent trend throughout Australia has been to develop multi-purpose indoor public aquatic centres in favour of outdoor pools. Such major policy and planning decisions often rely on consultants' feasibility studies, yet there is limited comprehensive industry-wide data available on which to base such decisions. The industry-wide performance measures discussed in this paper help fill this void by providing objective data to support the contention that multi-purpose indoor aquatic centres tend to outperform centres with solely outdoor pools. The key indicators of performance are based on financial viability and community participation data for a sample of Australian public aquatic centres.

Efforts to respond to performance-based accountability mandates for public health emergency preparedness have been hindered by a weak evidence base linking preparedness activities with response outcomes. We describe an approach to measure development that was successfully implemented in the Centers for Disease Control and Prevention Public Health Emergency Preparedness Cooperative Agreement. The approach leverages insights from process mapping and experts to guide measure selection, and provides mechanisms for reducing performance-irrelevant variation in measurement data. Also, issues are identified that need to be addressed to advance the science of measurement in public health emergency preparedness.

The lack of frequent real-world opportunities to study preparedness for large-scale public health emergencies has hindered the development of an evidence base to support best practices, performance measures, standards, and other tools needed to assess and improve the nation’s multibillion dollar investment in public health preparedness. In this article, we argue that initial funding priorities for public health systems research on preparedness should focus on using engineering-style methods to identify core preparedness processes, developing novel data sources and measures based on smaller-scale proxy events, and developing performance improvement approaches to support the translation of research into practice within the wide variety of public health systems found in the nation. (Disaster Med Public Health Preparedness. 2008;2:247–250)

We consider the simulation of transient performance measures of high reliable fault-tolerant computer systems. The most widely used mathematical tools to model the behavior of these systems are Markov processes. Here, we deal basically with the simulation of the mean time to failure (MTTF) and the reliability, R(t), of the system at time t. Some variance reduction techniques are used to reduce the simulation time. We will combine two of these techniques: Importance Sampling and Conditioning Technique. The resulting hybrid algorithm performs significant reduction of simulation time and gives stables estimations.

There are some generalised semi-Markov processes (GSMP) which are insensitive, that is the value of some performance measures for the system depend only on the mean value of lifetimes and not on their actual distribution. In most cases this is not true and a performance measure can take on a number of values depending on the lifetime distributions. In this paper we present a method for finding tight bounds on the sensitivity of performance measures for the class of GSMPs with a single generally distributed lifetime. Using this method we can find upper and lower bounds for the value of a function of the stationary distribution as the distribution of the general lifetime ranges over a set of distributions with fixed mean. The method is applied to find bounds on the average queue length of the Engset queue and the time congestion in the GI/M/n/n queueing system.