Search Results (6)

Due to increased container traffic, the problems of congestion at terminal gates generate serious air pollution and decrease terminal efficiency. To address this issue, many terminals are implementing a truck appointment system (TAS) based on several concepts. Our work addresses gate congestion at a container terminal. A conceptual model was developed to identify system components and interactions, analyzing container flow from both static and dynamic perspectives. A truck appointment system (TAS) was modeled to optimize waiting times using a non-stationary approach. Compared to existing methods, our TAS introduces a more adaptive scheduling mechanism that dynamically adjusts to fluctuating truck arrivals, reducing peak congestion and improving resource utilization. Unlike traditional static appointment systems, our approach helps reduce truckers’ dissatisfaction caused by the deviation between the preferred time and the assigned one, leading to smoother operations. Various genetic algorithms were tested, with a hybrid genetic–tabu search approach yielding better results by improving solution stability and reducing computational time. The model was applied and adapted to the Port of Casablanca using real-world data. The results clearly highlight a significant potential to enhance sustainability, with an annual reduction of 785 tons of CO₂ emissions from a total of 1281 tons. Regarding trucker dissatisfaction, measured by the percentage of trucks rescheduled from their preferred times, only 7.8% of arrivals were affected. This improvement, coupled with a 62% decrease in the maximum queue length, further promotes efficient and sustainable operations. Full article

We consider a non-standard class of Markovian time: varying infinite capacity queues with possibly heterogeneous servers and impatience. We assume that during service time, a customer may switch to the faster server (with no delay), when such a server becomes available and no other customers are waiting. As a result, customers in the queue may become impatient and leave it. Under this setting and with certain restrictions on the intensity functions, the quantity of interest, the total number of customers in the system, is the level-dependent birth-and-death process (BPD). In this paper, for the first time in the literature, explicit upper bounds for the distance between two probability distributions of this BDP are obtained. Using the obtained ergodicity bounds in combination with the sensitivity bounds, we assess the stability of BDP under perturbations. Truncation bounds are also given, which allow for numerical solutions with guaranteed truncation errors. Finally, we provide numerical results to support the findings. Full article

We performed a non-stationary analysis of a class of buffer management schemes for TCP/IP networks, in which the arriving packets were rejected randomly, with probability depending on the queue length. In particular, we derived formulas for the packet waiting time (queuing delay) and the intensity of packet losses as functions of time. These results allow us to observe how the evolution of the waiting time and losses depend on initial conditions (e.g., the full buffer) and system parameters (e.g., dropping probabilities, load, packet size distribution). As side results, the stationary waiting time and packet loss probability were obtained. Numerical examples demonstrate applicability of the theoretical results. Full article

A multiple-airport system (MAS) consists of more than two airports in a metropolitan area under a large block of terminal airspace that is managed by one or two air traffic control units. When the capacity of an airport or of the terminal airspace drops, flight delays occur in the MAS system. A quick estimation and predication of traffic congestion in the MAS is important yet challenging. This paper aims to develop a queuing network model of MAS using point-wise stationary queues. The model analyzes the changes of non-stationary queues under the principle of flow conservation to capture flight delay propagation in the system. Regression analyses are performed to examine the relationship between the arrival and departure efficiencies of different airports. The model is validated with the data of Guangdong–Hong Kong–Macao Greater Bay Area airports. Simulation results show that the model can effectively estimate flight delays in the MAS. Full article

The data transmission in wireless networks is usually analyzed under the assumption of non-stationary rates. Nevertheless, they strictly depend on the time of day, that is, the intensity of arrival and daily workload profiles confirm this fact. In this article, we consider the process of downloading a file within a single network segment and unsteady speeds—for arrivals, file sizes, and losses due to impatience. To simulate the scenario, a queuing system with elastic traffic with non-stationary intensity is used. Formulas are given for the main characteristics of the model: the probability of blocking a new user, the average number of users in service, and the queue. A method for calculating the boundaries of convergence of the model is proposed, which is based on the logarithmic norm of linear operators. The boundaries of the rate of convergence of the main limiting characteristics of the queue length process were also established. For clarity of the influence of the parameters, a numerical analysis was carried out and presented. Full article

This paper investigates the characteristics of the MAP/M/1/N queuing system in the transient mode. The matrix method for solving the Kolmogorov equations is proposed. This method makes it possible, in general, to obtain the main characteristics of the considered queuing system in a non-stationary mode: the probability of losses, the time of the transient mode, the throughput, and the number of customers in the system at time t. The developed method is illustrated by numerical calculations of the characteristics of the $MAP/M/1/3$ system in the transient mode. Full article