Queing Theory, a Tool for Polio Eradication in Nigeria

To curb the spread of contagious diseases and the recent polio outbreak in Nigeria, health departments must set up and operate clinics to dispense medications or vaccines. Residents arrive according to an external (not necessarily Poisson) Arrival process to the clinic. When a resident arrives, he goes to the first workstation, based on his or her information, the resident moves from one workstation to another in the clinic. The queuing network is decomposed by estimating the performance of each workstation using a combination of exact and approximate models. A key contribution of this research is to introduce approximations for workstations with batch arrivals and multiple parallel servers, for workstations with batch service processes and multiple parallel servers, and for self service workstations. We validated the models for likely scenarios using data collected from one of the states vaccination clinics in the country during the vaccination exercises.

Optimal replacement policy under cumulative damage model and strength degradation with applications

In many real-life scenarios, system failure depends on dynamic stress-strength interference, where strength degrades and stress accumulates concurrently over time. In this paper, we consider the problem of finding an optimal replacement strategy that balances the cost of replacement with the cost of failure and results in the minimum expected cost per unit time under cumulative damage model with strength degradation. In the most general setting, we propose to find optimal choices of three thresholds on operation time, number of arriving shocks and amount of cumulative damage such that replacement of the system due to failure or reaching any of the three thresholds, whichever occurs first, results in the minimum expected cost per unit time. The existing recommendations are applicable only under the assumption of Exponential damage distribution including Poisson arrival of shocks and/or with fixed strength. As theoretical evaluation of the expected cost per unit time turns out to be very complicated, a simulation-based algorithm is proposed to evaluate the expected cost rate and find the optimal replacement strategy. The proposed method is easy to implement having wider domain of application including non-Poisson arrival of shocks and non-Exponential damage distributions. For illustration, the proposed method is applied to real case studies on mailbox and cell-phone battery experiments.

On optimal stochastic jumps in multi server queue with impatient customers via stochastic control

<p style='text-indent:20px;'>In this paper, a queuing system as multi server queue, in which customers have a deadline and they request service from a random number of identical severs, is considered. Indeed there are stochastic jumps, in which the time intervals between successive jumps are independent and exponentially distributed. These jumps will be occurred due to a new arrival or situation change of servers. Therefore the queuing system can be controlled by restricting arrivals as well as rate of service for obtaining optimal stochastic jumps. Our model consists of a single queue with infinity capacity and multi server for a Poisson arrival process. This processes contains deterministic rate <inline-formula><tex-math id="M1">\begin{document}$ \lambda(t) $\end{document}</tex-math></inline-formula> and exponential service processes with <inline-formula><tex-math id="M2">\begin{document}$ \mu $\end{document}</tex-math></inline-formula> rate. In this case relevant customers have exponential deadlines until beginning of their service. Our contribution is to extend the Ittimakin and Kao's results to queueing system with impatient customers. We also formulate the aforementioned problem with complete information as a stochastic optimal control. This optimal control law is found through dynamic programming.</p>

On Periodic Dividends for the Classical Risk Model with Debit Interest

A periodic dividend problem is studied in this paper. We assume that dividend payments are made at a sequence of Poisson arrival times, and ruin is continuously monitored. First of all, three integro-differential equations for the expected discounted dividends are obtained. Then, we investigate the explicit expressions for the expected discounted dividends, and the optimal dividend barrier is given for exponential claims. A similar study on a generalized Gerber–Shiu function involving the absolute time is also performed. To demonstrate the existing results, we give some numerical examples.

A Comprehensive Review and Analysis of Key Heuristics of Load Balancing Techniques in Cloud Computing

Background: The field of cloud computing has been evolving for over a decade now. Load balancing is an important component of cloud computing. Load balancing implies scheduling of cloudlets (tasks) on virtual machines. Since this is a NP-hard problem, various heuristics for load balancing have been proposed in the research literature. The heuristics have been categorized, simulated and benchmarked in various ways; however, the information is scattered across many review articles. Objective: This review aims to bring a broad range of load balancing heuristics found in the research literature under one umbrella. It includes a comprehensive list of heuristics, a holistic set of criteria for their classification, and some key performance metrics and simulation tools used for their benchmarking. An illustration of fair and comprehensive comparison of heuristics is provided using CloudSim Plus, a recent and advanced simulation tool. Method: The simulations performed with CloudSim Plus employ a generic model of task and machine heterogeneity with Poisson arrival of cloudlets and exponential distribution of cloudlet length to emulate actual cloud-computing scenarios. The simulation results in terms of key performance metrics are used to compare four centralized load balancing heuristics including Join Shortest Queue (JSQ), Join Idle Queue (JIQ), Round Robin and Minimum Completion Time (MCT).