Queuing Theory in Traffic Management System

In cities where the number of vehicles has consistently expanded faster than the transportation infrastructure available to serve them. More on queuing theory and its crucial application has been discussed in the current study. In Thudiyalur, Gandhipuram, and Periyanaickenpalayam, all in Coimbatore, this research examines the usefulness of queuing theory in the field of traffic management. The concept of traffic intensity isapplied to a set of areas in queuing theory in this study. Keywords: Traffic intensity, Queuing theory, Single server Poisson model

A Probabilistic Approach to Growth Networks

Single-class closed queueing networks, consisting of infinite-server and single-server queues with exponential service times and probabilistic routing, admit product-from solutions. Such solutions, although seemingly tractable, are difficult to characterize explicitly for practically relevant problems due to the exponential combinatorial complexity of its normalization constant (partition function). In “A Probabilistic Approach to Growth Networks,” Jelenković, Kondev, Mohapatra, and Momčilović develop a novel methodology, based on a probabilistic representation of product-form solutions and large-deviations concentration inequalities, which identifies distinct operating regimes and yields explicit expressions for the marginal distributions of queue lengths. From a methodological perspective, a fundamental feature of the proposed approach is that it provides exact results for order-one probabilities, even though the analysis involves large-deviations rate functions, which characterize only vanishing probabilities on a logarithmic scale.

Analysis of a Discrete-Time Queueing Model with Disasters

Queueing models with disasters can be used to evaluate the impact of a breakdown or a system reset in a service facility. In this paper, we consider a discrete-time single-server queueing system with general independent arrivals and general independent service times and we study the effect of the occurrence of disasters on the queueing behavior. Disasters occur independently from time slot to time slot according to a Bernoulli process and result in the simultaneous removal of all customers from the queueing system. General probability distributions are allowed for both the number of customer arrivals during a slot and the length of the service time of a customer (expressed in slots). Using a two-dimensional Markovian state description of the system, we obtain expressions for the probability, generating functions, the mean values, variances and tail probabilities of both the system content and the sojourn time of an arbitrary customer under a first-come-first-served policy. The customer loss probability due to a disaster occurrence is derived as well. Some numerical illustrations are given.

On A Single Server Queue with Two-Stage First Essential Service Followed by One of the Two Types of Additional Optional Service and Optional Deterministic Server Vacations

We study the steady state behavior of a batch arrival single server queue in which the first service consisting of two stages with general service times G1 and G2 is compulsory. After completion of the two stages of the first essential service, a customer has the option of choosing one of the two types of additional service with respective general service times G1 and G2 . Just after completing both stages of first essential service with or without one of the two types of additional optional service, the server has the choice of taking an optional deterministic vacation of fixed (constant) length of time. We obtain steady state probability generating functions for the queue size for various states of the system at a random epoch of time in explicit and closed forms. The steady state results of some interesting special cases have been derived from the main results.

Usage of pedestrian overpass in Akure, Nigeria

Background This study addressed the safety challenge, motivation, and utilization factors regarding the usage of the pedestrian overpass by different people of dissimilar ages alongside Oba Adeshida road at Oja-Oba (Oba market) in Akure, Ondo State, Nigeria. It addressed the following objectives: determined the value of the pedestrian overpass as used by people of different ages; examined the reasons for using the pedestrian overpass in Akure; and examined the performance level of a pedestrian overpass in Akure. Methods In total, 384 users (who used the bridge) were purposively sampled for questionnaire administration, but 324 users participated in the questionnaire, which included multiple-choice and open-ended questions. Also, personal observation was employed for queue analysis. The “Semantic Differential Scale” and single-server queue system for the single queue were employed for data analysis. Conclusions In Akure, there was low or no usage of the pedestrian overpass when the road median was made use of metal and low concrete; but when the road median was made use of high concrete barrier, there was high usage of the pedestrian overpass. It also revealed that the engineering design of the pedestrian overpass is low compared to the contemporary design solutions in addressing the urban societal needs. The pedestrian overpass was used frequently and every day because it provides access to the car park, market, and central mosque. The performance of the pedestrian overpass in Akure is 105% which indicates that the pedestrian overpass is over-utilized by a pedestrian. It is recommended that there is a need to construct another pedestrian overpass to enhance the efficiency of the structure. The existing and future pedestrian overpass should be redesigned to constitute interesting aesthetics and architectural solutions that could harmonize with the environment and enhance flow of the disabled persons.