Generalized gap acceptance models for unsignalized intersections

This paper contributes to the modeling and analysis of unsignalized intersections. In classical gap acceptance models vehicles on the minor road accept any gap greater than the CRITICAL gap, and reject gaps below this threshold, where the gap is the time between two subsequent vehicles on the major road. The main contribution of this paper is to develop a series of generalizations of existing models, thus increasing the model's practical applicability significantly. First, we incorporate {driver impatience behavior} while allowing for a realistic merging behavior; we do so by distinguishing between the critical gap and the merging time, thus allowing MULTIPLE vehicles to use a sufficiently large gap. Incorporating this feature is particularly challenging in models with driver impatience. Secondly, we allow for multiple classes of gap acceptance behavior, enabling us to distinguish between different driver types and/or different vehicle types. Thirdly, we use the novel M$^X$/SM2/1 queueing model, which has batch arrivals, dependent service times, and a different service-time distribution for vehicles arriving in an empty queue on the minor road (where `service time' refers to the time required to find a sufficiently large gap). This setup facilitates the analysis of the service-time distribution of an arbitrary vehicle on the minor road and of the queue length on the minor road. In particular, we can compute the MEAN service time, thus enabling the evaluation of the capacity for the minor road vehicles

Analysis of Fluid Queues Using Level Crossing Methods ID: 11563

This dissertation is concerned with the application of the level crossing method on fluid queues driven by a background process. The basic assumption of the fluid queue in this thesis is that during the busy period of the driving process, the fluid content fills at net rate r_1, and during the idle period of the driving process, the fluid content, if positive-valued, empties at a rate r_2. Moreover, nonempty fluid content, leaks continuously at a rate r_2. The fluid models considered are: the fluid queue driven by an M/G/1 queue in Chapter 2, the fluid queue driven by an M/G/1 queue with net input and leaking rate depending on fluid level, and type of arrivals in the driving M/G/1 queue, in chapter 3, and the fluid queue driven by an M/G/1 queue with upward fluid jumps in Chapter 4. In addition, a triangle diagram has been introduced in this thesis as a technique to visualize the proportion of time that the content of the fluid queue is increasing or decreasing during nonempty cycles. Finally, we provide several examples on how the probability density function of the fluid level is related to the probability density function of the waiting time of M/G/1 queues with different disciplines

Two approximations for the steady-state probabilities and the sojourn-time distribution of the M/D/c queue with state-dependent feedback

In the M/D/c queue with state-dependent feedback, a customer is only allowed to depart from the system if his service has been successful. Otherwise, the customer must be re-serviced immediately. The probability that a customer's service is successful depends on the number of customers in service at the moment the service is finished. The application behind this type of feedback queue is a real-time database where transactions must be rerun if their data was changed by other transactions during the execution. In this paper, two different approximations for the steady-state probabilities and the sojourn-time distribution of the M/D/c queue with state-dependent feedback are studied. The first approximation is based on an embedded Markov chain and uses the well-known residual-life approximation for the remaining service times of the customers in service. The second approximation is similar to the exact analysis of the ordinary M/D/c queue. Comparison with simulation shows, that both approximations are very accurate for a wide range of system parameters, even for heavily loaded systems

A class of multi-server queueing systems with unreliable servers: Models and application.

Where queueing systems with unreliable servers are concerned, most research that has been done focuses on one-server systems or systems with a Poisson arrival process and exponential service time. However, in some situations we need to consider non-exponential service time or service rate changes with the number of available servers. These are the queueing systems that are discussed in this thesis, none of which has ever been discussed in the literature. Since the phase type distribution is more general than the exponential distribution and captures most features of a general distribution, the phase type distributed service time is considered in unreliable queueing systems such as M/PH/n and M/PH/n/c. For the M/PH/n queueing system with unreliable servers, the mathematical model, stability condition analysis, stationary distribution calculation, computer programs and examples are all presented. For the M/PH/n/c queueing system with server failures, a finite birth-and-death mathematical model is built and the stationary distribution and performance evaluation measurements are calculated. Computer programs are developed and an example is given to demonstrate the application of this queueing system. (Abstract shortened by UMI.)Dept. of Industrial and Manufacturing Systems Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2003 .Y375. Source: Masters Abstracts International, Volume: 43-01, page: 0295. Adviser: Attahiru S. Alfa. Thesis (M.A.Sc.)--University of Windsor (Canada), 2004

Energy-saving policies for temperature-controlled production systems with state-dependent setup times and costs

There are numerous practical examples of production systems with servers that require heating in order to process jobs. Such production systems may realize considerable energy savings by temporarily switching off the heater and building up a queue of jobs to be processed later, at the expense of extra queueing costs. In this paper, we optimize this trade-off between energy and queueing costs. We model the production system as an M/G/1 queue with a temperature-controlled server that can only process jobs if a minimum production temperature is satisfied. The time and energy required to heat a server depend on its current temperature, hence the setup times and setup costs for starting production are state dependent. We derive the optimal policy structure for a fluid queue approximation, called a wait-heat-clear policy. Building upon these insights, for the M/G/1 queue we derive exact and approximate costs for various intuitive types of wait-heat-clear policies. Numerical results indicate that the optimal wait-heat-clear policy yields average cost savings of over 40% compared to always keeping the server at the minimum production temperature. Furthermore, an encouraging result for practice is that simple heuristics, depending on the queue length only, have near-optimal performance

Queues with random back-offs

We consider a broad class of queueing models with random state-dependent vacation periods, which arise in the analysis of queue-based back-off algorithms in wireless random-access networks. In contrast to conventional models, the vacation periods may be initiated after each service completion, and can be randomly terminated with certain probabilities that depend on the queue length. We examine the scaled queue length and delay in a heavy-traffic regime, and demonstrate a sharp trichotomy, depending on how the activation rate and vacation probability behave as function of the queue length. In particular, the effect of the vacation periods may either (i) completely vanish in heavy-traffic conditions, (ii) contribute an additional term to the queue lengths and delays of similar magnitude, or even (iii) give rise to an order-of-magnitude increase. The heavy-traffic asymptotics are obtained by combining stochastic lower and upper bounds with exact results for some specific cases. The heavy-traffic trichotomy provides valuable insight in the impact of the back-off algorithms on the delay performance in wireless random-access networks