Steady State Analysis Of An M/D/2 Queue With Bernoulli Schedule Server Vacations

We examine an M/D/2 queue with Bernoulli schedules and a single vacation policy. We have assumed Poisson arrivals waiting in a single queue and two parallel servers who provide identical deterministic service to customers on first-come, first-served basis. We consider two models; in one we assume that after completion of a service both servers can take a vacation while in the other we assume that only one may take a vacation. The vacation periods in both models are assumed to be exponential. We obtain steady state probability generating functions of system size for various states of the servers

Sleep Mode Analysis via Workload Decomposition

The goal of this paper is to establish a general approach for analyzing queueing models with repeated inhomogeneous vacations. The server goes on for a vacation if the inactivity prolongs more than the vacation trigger duration. Once the system enters in vacation mode, it may continue for several consecutive vacations. At the end of a vacation, the server goes on another vacation, possibly with a different probability distribution; if during the previous vacation there have been no arrivals. However the system enters in vacation mode only if the inactivity is persisted beyond defined trigger duration. In order to get an insight on the influence of parameters on the performance, we choose to study a simple M/G/1 queue (Poisson arrivals and general independent service times) which has the advantage of being tractable analytically. The theoretical model is applied to the problem of power saving for mobile devices in which the sleep durations of a device correspond to the vacations of the server. Various system performance metrics such as the frame response time and the economy of energy are derived. A constrained optimization problem is formulated to maximize the economy of energy achieved in power save mode, with constraints as QoS conditions to be met. An illustration of the proposed methods is shown with a WiMAX system scenario to obtain design parameters for better performance. Our analysis allows us not only to optimize the system parameters for a given traffic intensity but also to propose parameters that provide the best performance under worst case conditions

Heavy-traffic limits for Polling Models with Exhaustive Service and non-FCFS Service Order Policies

We study cyclic polling models with exhaustive service at each queue under a variety of non-FCFS local service orders, namely Last-Come-First-Served (LCFS) with and without preemption, Random-Order-of-Service (ROS), Processor Sharing (PS), the multi-class priority scheduling with and without preemption, Shortest-Job-First (SJF) and the Shortest Remaining Processing Time (SRPT) policy. For each of these policies, we rst express the waiting-time distributions in terms of intervisit-time distributions. Next, we use these expressions to derive the asymptotic waiting-time distributions under heavy-trac assumptions, i.e., when the system tends to saturate. The results show that in all cases the asymptotic wait

Sleep Mode Analysis via Workload Decomposition

The goal of this paper is to establish a general approach for analyzing queueing models with repeated inhomogeneous vacations. Theserver goes on for a vacation if the inactivity prolongs more than a vacation trigger duration. Once the system enters in vacation mode,it may continue for several consecutive vacation. At the end of a vacation, the server goes on another vacation, possibly with a {\emdifferent} probability distribution, if during the previous vacation there have been no arrivals. However the system enters in vacationmode only if the inactivity is persisted beyond a defined trigger duration. In order to get an insight on the influence of parameterson the performance, we choose to study a simple $M/G/1$ queue (Poisson arrivals and general independent service times) which hasthe advantage of being tractable analytically. The theoretical model is applied to the problem of power saving for mobile devices inwhich the sleep durations of a device correspond to the vacations of the server. Various system performance metrics such as the frameresponse time and the economy of energy are derived. A constrained optimization problem is formulated to maximize the economy of energy achieved in power save mode, with constraints as QoS conditions to be met. An illustration of the proposed methods is shown with a WiMAX system scenario to obtain design parameters for better performance. Our analysis allows us not only to optimize the system parameters for a given traffic intensity but also to propose parameters that provide the best performance under worst caseconditions

Modelling trauma hip fracture hospital activities

Hip fracture is the most common reason for an elderly person to be admitted to an acute orthopaedic ward. The main aim of this research is to provide a statistical evaluation of a hip fracture database, and then to use Operational Research (OR) techniques, using the statistical output, to model activities associated with the care of hip fracture patients. OR techniques employed in this thesis include simulation and queuing theory. This research focuses on hip fracture admissions to the University Hospital of Wales in Cardiff, with a primary aim of ascertaining whether the time between admission and surgical intervention has any impact upon patient outcome. Outcome is considered in terms of mortality, hospital length of stay and discharge destination. Statistical analyses are performed, via regression and CART analysis, to investigate length of stay and mortality variables. The results from these statistical tests are compiled, compared and investigated in more depth. Additionally, a principal component analysis is performed to investigate whether it would be feasible to reduce the dimensionality of the dataset, and subsequently principal component regression methodology is used to complement the output. Simulation is used to model activities in both the hip fracture ward and the trauma theatre. These models incorporate output from the statistical analysis and encompass complexities within the patient group and theatre process. The models are then used to test a number of ‘what-if’ type scenarios, including the future anticipated increase in demand. Finally, results from queuing theory are applied to the trauma theatre in order to determine a desired daily theatre allocation for these patients. Specifically, the M | G | 1 queuing system and results from queues with vacations are utilised. The thesis concludes with some discussion of how this research could be further expanded. In particular, two areas are considered; risk scoring systems and the Fenton-Wilkinson approximation