Busy period analysis of the level dependent PH/PH/1/K queue

In this paper, we study the transient behavior of a level dependent single server queuing system with a waiting room of finite size during the busy period. The focus is on the level dependent PH/PH/1/K queue. We derive in closed form the joint transform of the length of the busy period, the number of customers served during the busy period, and the number of losses during the busy period. We differentiate between two types of losses: the overflow losses that are due to a full queue and the losses due to an admission controller. For the M/PH/1/K, M/PH/1/K under a threshold policy, and PH/M/1/K queues, we determine simple expressions for their joint transforms

Accident Analysis of Ice Control Operations

Highway maintenance involves all work necessary to assure that the highway system is kept safe, open to traffic, and in proper working order. During winter, the removal of snow and ice from streets, roads, and highways is a major maintenance operation. With more than 135 million motor vehicles registered in the United States and roughly four million miles of roads and streets, local governments must be prepared to deal with the removal of snow and ice to insure public safety, and to reduce the adverse impact on the affected area’s economy. Snow and ice covered roads can paralyze the functioning of the community and pose a considerable threat to the public safety. They produce hazardous driving conditions which increase traffic deaths, injuries, and property damage. The general assumption has always been that snow and ice on highways causes accidents. There are a number of reasons for this assumption. Snow and ice reduce the coefficient of friction between the pavement and vehicle tires, making maneuvering of the vehicle very difficult and occasionally impossible. Ice is not always apparent to the motorist and is not uniform, so that the driver is not always prepared when he encounters an icy section on the roadway. Vehicle mobility is reduced, causing possible severe disruption of important public emergency services, such as fire, police, and ambulance operations. Without close attention to the effective removal of snow and ice from roads, the economy of the region involved will suffer, and traffic accidents will escalate. Most activities of individuals, industries, utilities, schools, and government activities are handicapped in social and economic ways during the duration of snow and ice conditions on roads and streets

Performance of ad hoc networks with two-hop relay routing and limited packet lifetime (extended version)

We consider a mobile ad hoc network consisting of three types of nodes (source, destination and relay nodes) and using the two-hop relay routing. This type of routing takes advantage of the mobility and the storage capacity of the nodes, called the relay nodes, in order to route packets between a source and a destination. Packets at relay nodes are assumed to have a limited lifetime in the network. Nodes are moving inside a bounded region according to some random mobility model. Closed-form expressions and asymptotic results when the number of nodes is large are provided for the packet delivery delay and for the energy needed to transmit a packet from the source to its destination. We also introduce and evaluate a variant of the two-hop relay protocol that limits the number of generated copies in the network. Our model is validated through simulations for two mobility models (random waypoint and random direction mobility models), and the performance of the two-hop routing and of the epidemic routing protocols are compared.\ud \u

Busy period analysis of the level dependent PH/PH/1/K queue

In this paper, we study the transient behavior of a level dependent PH/PH/1/K queue during the busy period. We derive in closed-form the joint transform of the length of the busy period, the number of customers served during the busy period, and the number of losses during the busy period. We differentiate between two types of losses: the over°ow losses that are due to a full queue and the losses due to an admission controller. For the M/PH/1/K, M/PH/1/K under a threshold policy, and PH/M/1/K queues we determine simple expressions for their joint transfor

Accident Analysis of Ice Control Operations - Abstract

This widely publicized study by Marquette University was the first of its kind in North America to document, with statistical validity, the direct benefits of deicing operations. It was patterned after a German study of the Technical University at Darmstadt during the late 1980s. The Marquette study was conducted during the winter of 1990-1991 in four states: New York, Illinois, Minnesota and Wisconsin. It covered a network of 520 miles of randomly selected twolane undivided highways and 50 miles of multi-lane divided freeways in the four states. The sections included were primarily rural or sub-urban. Data collection included estimated hourly traffic volumes, accidents, and operating parameters including the time and amount of de- icer used for equal 12 hour periods before and after “zero” hour (the hour of the actual spreading of deicer). The direct costs of the operation were also collected and calculated. Estimates of traffic volume reduction due to snow, travel time reduction and the costs associated with the above items were made using standard methodology. Data on winter events were obtained from event logs of the organizations and meteorological data available about the storms. The data collection included over 125 test sections in the four states and a total of 226 events, with almost 4600 sub-events (a single event on a single test section). For two-lane highway sections, the rate for all accidents was about eight times higher in the four hours before than it was in the four hours after “zero” hour (hours with the most significant difference). The rate for injury accidents was nine times higher before than after and for property damage only 7 times higher. There was an 88 percent reduction in accident costs in the four hour after period. The ratio of direct benefits to direct costs was about 6.5 to 1. The average direct costs were paid for after the first 71 vehicles used the highway, or paid for in about the first 25 minutes aft er the “zero” hour. For freeways, the rate for all accidents was about 4.5 times higher in the two hours before (hours with the most significant difference) than after “zero” hour. The rate for injury accidents was seven times higher before than after, and the rate for property damage accidents was two times higher before than after. There was an 88 percent reduction in accident costs in the two hour after period. The ratio of direct benefits to direct costs was about 3.5 to 1. The average direct costs were paid for after the first 280 vehicles used the highway, or paid for in about the first 35 minutes after “zero” hour. The study suggests this type of methodology for state-of-the-art cost benefit studies in the future. It is based on a doctoral dissertation completed at the University

Integrated service engineers and spare parts planning in the maintenance logistics

We analyze the integrated tactical capacity planning of spare parts supply and workforce allocation in maintenance logistics of advanced equipment. The equipment time-to-failure, spare parts replenishment time, and equipment repair time are random and independent of each other

Time-Limited and k-Limited Polling Systems: A Matrix Analytic Solution

In this paper, we will develop a tool to analyze polling systems with the autonomous-server, the time-limited, and the k-limited service discipline. It is known that these disciplines do not satisfy the well-known branching property in polling system, therefore, hardly any exact result exists in the literature for them. Our strategy is to apply an iterative scheme that is based on relating in closed-form the joint queue-length at the beginning and the end of a server visit to a queue. These kernel relations are derived using the theory of absorbing Markov chains. Finally, we will show that our tool works also in the case of a tandem queueing network with a single server that can serve one queue at a time