New approach for finding basic performance measures of single server queue

Consider the single server queue in which the system capacity is infinite and the customers are served on a first come, first served basis. Suppose the probability density functio

Repairable queue with non-exponential service time and variable breakdown rates

Consider a single server queue in which the service station may breakdown according to a Poisson process with rates γ in busy time and γ’ in idle time respectively. After a breakdown, the service station will be repaired immediately and the repair time is assumed to have an exponential distribution with rate δ. Suppose the arrival time has an exponential distribution with rate λ, and the probability density function g(t) and the cumulative distribution function G(t) of the service time are such that the rate g(t)/[1 – G(t)] tends to a constant as t tends to infinity. When the queue is in a stationary state, we derive a set of equations for the probabilities of the queue length and the states of the arrival and service processes. Solving the equations, we obtain approximate results for the stationary probabilities which can be used to obtain the stationary queue length distribution of the syste

Maintenance of deteriorating non-exponential single server queue / Koh Siew Khew

Consider the single server queue in which the system capacity is infinite and the customers are served on a first come, first served basis. The case of a system without deterioration is first studied. The stationary queue length distribution and the stationary waiting time distribution are derived for the system in which the service time and interarrival time distributions are assumed to have constant asymptotic rates. The results found are verified by using simulation. Next consider a system in which the server would deteriorate due to random shocks and the seriously affected server will be sent for repair. A similar method is applied for deriving the stationary queue length distribution in a system in which the interarrival time distribution (or service time) is assumed to have a constant asymptotic rate while the service time (or interarrival time) remains exponentially distributed. From the stationary queue length distribution, a number of other characteristics can be derived. These include the sojourn time distribution of a customer who arrives when the queue is in a stationary state, and the expected length of the duration between two successive repair completions. From these distributions and expected length, the value of the specified maintenance level is found such that the long run average cost is minimized

Home Activities Sequence Pattern Analysis

The elderly population in most of the countries has risen from year to year. Number of elderlies that staying alone at home also increase accordingly since the number of children in one family is decreasing. The cost of hiring caregivers is normally expensive and might cause financial burden to a family in the long-term. Fortunately, with advance technology, alternative approaches such as Global Monitoring System, smart clothing as well as embedded health care system in smart phone and smart watch could be the alternative approaches to monitor the health of some elderly that is able to live alone. The most feasible and cost-saving approach for in-house monitoring should be setting up sensors at different locations in a smart home for independent elderly that stay alone. Daily activities recorded through the sensors can be collected and analyzed to detect if there is any anomaly found. In this paper, analysis of staying alone elderly’s daily activities and behaviors are performed. This analysis is important to further developing suitable model that can be used to detect the anomalies in their routine home activity patterns

An alternative approach in finding the stationary queue length distribution of a queueing system with negative customers

A single-server queueing system with negative customers is considered in this paper. One positive customer will be removed from the head of the queue if any negative customer is present. The distribution of the interarrival time for the positive customer is assumed to have a rate that tends to a constant as time t tends to infinity. An alternative approach will be proposed to derive a set of equations to find the stationary probabilities. The stationary probabilities will then be used to find the stationary queue length distribution. Numerical examples will be presented and compared to the results found using the analytical method and simulation procedure. The advantage of using the proposed alternative approach will be discussed in this paper

An alternative approach in finding the stationary queue length distribution of a queueing system with negative customers

A single-server queueing system with negative customers is considered in this paper. One positive customer will be removed from the head of the queue if any negative customer is present. The distribution of the interarrival time for the positive customer is assumed to have a rate that tends to a constant as time t tends to infinity. An alternative approach will be proposed to derive a set of equations to find the stationary probabilities. The stationary probabilities will then be used to find the stationary queue length distribution. Numerical examples will be presented and compared to the results found using the analytical method and simulation procedure. The advantage of using the proposed alternative approach will be discussed in this paper

Stationary queue length distribution of a continuous-time queueing system with negative arrival

This paper studies a continuous-time single-server infinite capacity queueing system with two types of customer: positive and negative customers. Positive customers are ordinary customers that receives service in the server. A negative customer that arrives to the system according to a Poisson process with rate γ will remove one positive customer at the head upon its arrival. By assuming that the interarrival time and service time distributions tend to a constant when time t goes to infinity, a set of equations will be derived by using an alternative approach to find the stationary queue length distribution. Numerical results obtained by the alternative approach will be compared to those obtained by the existing method and verified by the simulation procedure

Repairable Queue with Non-exponential Interarrival Time and Variable Breakdown Rates

This paper considers a single server queue in which the service time is exponentially distributed and the service station may breakdown according to a Poisson process with the rates γ and γ' in busy period and idle period respectively. Repair will be performed immediately following a breakdown. The repair time is assumed to have an exponential distribution. Let g(t) and G(t) be the probability density function and the cumulative distribution function of the interarrival time respectively. When t tends to infinity, the rate of g(t)/[1 – G(t)] will tend to a constant. A set of equations will be derived for the probabilities of the queue length and the states of the arrival, repair and service processes when the queue is in a stationary state. By solving these equations, numerical results for the stationary queue length distribution can be obtained