Transient handover blocking probabilities in road covering cellular mobile networks

This paper investigates handover and fresh call blocking probabilities for subscribers moving along a road in a traffic jam passing through consecutive cells of a wireless network. It is observed and theoretically motivated that the handover blocking probabilities show a sharp peak in the initial part of a traffic jam roughly at the moment when the traffic jam starts covering a new cell. The theoretical motivation relates handover blocking probabilities to blocking probabilities in the M/D/C/C queue with time-varying arrival rates. We provide a numerically efficient recursion for these blocking probabilities. \u

Stationary distributions of the multi-type ASEP

We give a recursive construction of the stationary distribution of multi-type asymmetric simple exclusion processes on a finite ring or on the infinite line $Z$. The construction can be interpreted in terms of "multi-line diagrams" or systems of queues in tandem. Let $q$ be the asymmetry parameter of the system. The queueing construction generalises the one previously known for the totally asymmetric ($q=0$) case, by introducing queues in which each potential service is unused with probability $q^k$ when the queue-length is $k$. The analysis is based on the matrix product representation of Prolhac, Evans and Mallick. Consequences of the construction include: a simple method for sampling exactly from the stationary distribution for the system on a ring; results on common denominators of the stationary probabilities, expressed as rational functions of $q$ with non-negative integer coefficients; and probabilistic descriptions of "convoy formation" phenomena in large systems.Comment: 54 pages, 4 figure

Strategy-based dynamic assignment in transit networks with passenger queues

This thesis develops a mathematical framework to solve the problem of dynamic assignment in densely connected public transport (or transit – the two words are interchangeably used) networks where users do not time their arrival at a stop with the lines’ timetable (if any is published). In the literature there is a fairly broad agreement that, in such transport systems, passengers would not select the single best itinerary available, but would choose a travel strategy, namely a bundle of partially overlapping itineraries diverging at stops along different lines. Then, they would follow a specific path depending on what line arrives first at the stop. From a graph-theory point of view, this route-choice behaviour is modelled as the search for the shortest hyperpath (namely an acyclic sub-graph which includes partially overlapping single paths) to the destination in the hypergraph that describes the transit network. In this thesis, the hyperpath paradigm is extended to model route choice in a dynamic context, where users might be prevented from boarding the lines of their choice because of capacity constraints. More specifically, if the supplied capacity is insufficient to accommodate the travel demand, it is assumed that passenger congestion leads to the formation of passenger First In, First Out (FIFO) queues at stops and that, in the context of commuting trips, passengers have a good estimate of the expected number of vehicle passages of the same line that they must let go before being able to board. By embedding the proposed demand model in a fully dynamic assignment model for transit networks, this thesis also fills in the gap currently existing in the realm of strategy-based transit assignment, where – so far – models that employ the FIFO queuing mechanism have proved to be very complex, and a theoretical framework for reproducing the dynamic build-up and dissipation of queues is still missing.Open Acces

A time dependent performance model for multihop wireless networks with CBR traffic

In this paper, we develop a performance modeling technique for analyzing the time varying network layer queueing behavior of multihop wireless networks with constant bit rate traffic. Our approach is a hybrid of fluid flow queueing modeling and a time varying connectivity matrix. Network queues are modeled using fluid-flow based differential equation models which are solved using numerical methods, while node mobility is modeled using deterministic or stochastic modeling of adjacency matrix elements. Numerical and simulation experiments show that the new approach can provide reasonably accurate results with significant improvements in the computation time compared to standard simulation tools. © 2010 IEEE

Statistical Queuing Theory with Some Applications

An overview of theory of queues, single node and in network, is presented in this paper. In addition some applications are outlined. Some very well-known and others more uncommon

Simulation of Congestion Phenomena and Strategic Passenger Behaviour on Transit Networks

This article focuses on the simulation of transit networks, including passengers' congestion phenomena and strategic behaviour, as a tool for planning and operation. Specifically, it describes a model of user equilibrium on large-scale transit networks considering on-board overcrowding, queuing at stops and dwelling delay, and representing in addition the effects of random events, such as the availability of seats and the waiting of vehicles, through hyperarcs. The assignment algorithm computes a strategy-based user equilibrium with implicit hyperpath enumeration by solving a fixed-point formulation, through a gradient projection method, which highly improves convergence performance. The model was implemented in.net as a dll that uses the software PTV Visum as I/O source. This article will focus on the model formulation and its capability of reproducing the target phenomena, while the results of model validation and testing will be described in a following paper

Simulation of Congestion Phenomena and Strategic Passenger Behaviour on Transit Networks

Abstract This article focuses on the simulation of transit networks, including passengers' congestion phenomena and strategic behaviour, as a tool for planning and operation. Specifically, it describes a model of user equilibrium on large-scale transit networks considering on-board overcrowding, queuing at stops and dwelling delay, and representing in addition the effects of random events, such as the availability of seats and the waiting of vehicles, through hyperarcs. The assignment algorithm computes a strategy-based user equilibrium with implicit hyperpath enumeration by solving a fixed-point formulation, through a gradient projection method, which highly improves convergence performance. The model was implemented in .net as a dll that uses the software PTV Visum as I/O source. This article will focus on the model formulation and its capability of reproducing the target phenomena, while the results of model validation and testing will be described in a following paper