Queue-length synchronization in a communication networks

We study synchronization in the context of network traffic on a $2-d$ communication network with local clustering and geographic separations. The network consists of nodes and randomly distributed hubs where the top five hubs ranked according to their coefficient of betweenness centrality (CBC) are connected by random assortative and gradient mechanisms. For multiple message traffic, messages can trap at the high CBC hubs, and congestion can build up on the network with long queues at the congested hubs. The queue lengths are seen to synchronize in the congested phase. Both complete and phase synchronization is seen, between pairs of hubs. In the decongested phase, the pairs start clearing, and synchronization is lost. A cascading master-slave relation is seen between the hubs, with the slower hubs (which are slow to decongest) driving the faster ones. These are usually the hubs of high CBC. Similar results are seen for traffic of constant density. Total synchronization between the hubs of high CBC is also seen in the congested regime. Similar behavior is seen for traffic on a network constructed using the Waxman random topology generator. We also demonstrate the existence of phase synchronization in real Internet traffic data.Comment: 13 Pages, 15 figure

Queue Management Project Model: Strategies for the Management of Queues at Upstream Junctions

This Working Paper is one of a series representing work under a SERC grant on queue management strategies for urban traffic control systems, whose objectives are:- (i)to generalise the strategies developed in an earlier study of queue management; (ii)to develop a computer graphics based representation of queue propagation and management; (iii)to test the strategies' applicability and performance in UK networks; (iv)to investigate their incorporation into standard signal optimisation programs. The study is based on earlier work in Bangkok (May et al, 1988) also funded by SERC, in which queue management measures were developed by trial and error to allow for the fact that queues from downstream junctions frequently blocked upstream junctions and could, as a result, unnecessarily obstruct crossing movements thereby reducing junction capacity and spreading congestion to other areas. The methods developed in that study involved:- (i)predicting the growth and decline of queues from downstream junctions; (ii)estimating the speeds of the starting and stopping waves which determine (i); (iii)identifying the most appropriate stage at the upstream junction in which queues should arrive; (iv)identifying the most appropriate time in that stage during which queues should be present; (v)adjusting the split between stages to allow for loss of throughput in blocked stages; (vi)adjusting the cycle time as necessary in the light of (v). It was steps (iii) and (iv) which involved the greatest element of trial and error, and it was accepted that further work was needed to identify alternative strategies for determining:- (i)during which stage to allow queues to block an upstream junction; (ii)how to adjust the stage timings at that junction to allow for the loss of capacity. This paper reviews these approaches and makes recommendations. It considers first of all, in Section 2, the options at an individual junction. It then considers in Section 3, the application of these options in a range of increasingly complex networks

Area Speed Flow Relationships: Initial SATURN Results for the Ring-Radial Network

This paper is one of a series of ITS working papers and technical notes describing the methodology and results of the EPSRC funded project "The definition of capacity in urban road networks : The role of area speed flow relationships". The objectives of the project were to investigate the interaction between vehicle-hours and vehicle-km within a network as the demand for travel increases; to develop improved area speed flow relationships; to use the relationships to explain the process by which networks reach capacity; and to assess the significance for the evaluation of road pricing policies. The approach used was to collect the vehicle-hours and the vehicle-km directly from a simulation model and thus create relationships between supply and demand in terms of veh-hours/hr and veh-km/hr demanded and also between times per trip and trips demanded. During the project two models were used. The first was a micro-simulation model called NEMIS. This model was used on hypothetical networks ranging from single link to a six by six grid and finally a ring-radial network. The networks were used to study the effects of changes in OD pattern and the effects of varying capacity on the resulting speed flow measures. The second model used was SATURN. This model was used to study the same ring-radial as before and a full SATURN model of Cambridge. The SATURN results were then taken one step further in that they were used to create an aggregate model of each network using SATURN in buffer only mode. The related papers discuss issues such as network aggregation. Note that the methodology and terminology was developed as the study progressed and that in particular the method varies between application of the two distinct models. The reader is directed to the attached appendix A for a full list of publications arising from this project

Area Speed-Flow Relationships by Micro-Simulation: Sensitivity Issues and Problems with the Tracking Approach When Extended to Multi-Zone Networks

This working paper is the third in a series relating to the EPSRC funded project, " The definition of capacity in urban road networks : the role of area speed-flow relationships". The paper looks at the sensitivity of the results to the process of modelling blocking-back in NEMIS, for the same 6x6 grid network described by May and Shepherd (1994b). First of all the blocking-back logic implemented in NEMIS is described. This logic was developed by Shepherd (1990) for use on an arterial network with the intention of blocking cross flows at signalised junctions. When implemented on grid networks with high demands and certain turning ratios this logic can lead to gridlock conditions. The logic implemented in NEMIS caused an irrecoverable gridlock condition i.e. once gridlock occurs it cannot be cleared. Although gridlock conditions may exist for short periods of time in the real world driver behaviour and or external factors combine to relieve the condition eventually. The results will be discussed with and without the blocking-back model implemented in NEMIS for matrix B - heavy inbound traffic. This work also revealed some problems with the tracking approach described by May and Shepherd (1994a) and the definition of demand when extended from single link/zone networks to multi-zone networks. One of the main problems was that of overlapping in the space-time domain, the amount of overlap increasing as demand is increased

A Review of Traffic Signal Control.

The aim of this paper is to provide a starting point for the future research within the SERC sponsored project "Gating and Traffic Control: The Application of State Space Control Theory". It will provide an introduction to State Space Control Theory, State Space applications in transportation in general, an in-depth review of congestion control (specifically traffic signal control in congested situations), a review of theoretical works, a review of existing systems and will conclude with recommendations for the research to be undertaken within this project

Stated Preference Analysis of Driver Route Choice Reaction To Variable Message Sign Information

Highway Authorities in many parts of the world have, for some years, been using variable message panels mounted above or beside the camageway to communicate short messages to motorists. Most such applications have been concerned with hazard warning and speed advice. However, their use to deliberately affect route choice is an area of great current interest. It is recognised that they have a potential role in managing demand to match the capacity available, not only to alleviate acute problems caused by roadworks and accidents, but also to contribute to satisfactory performance of networks operating close to capacity over extended periods of high, but variable, demand. The installation and operation of the panels is not cheap and there is a widespread belief that overuse, or inappropriate use, of the messages may lead to them losing their credibility with the motorists and thus ceasing to be effective. It is therefore very important to understand the likely response of motorists to various messages before displaying them and even before selecting sites for the installation of panels. A number of researchers have explored drivers' responses to traffic information and route advice offered via variable message signs (VMS). Evidence from traffic counts suggests that messages can persuade somewhere between 5% and 80% of drivers to divert. Clearly this range of estimates is far too wide to support the use of VMS for fine tuning the pattern of demand. A major contributor to the uncertainty, however, is the varying, and often unknown, proportion of drivers whose destination makes the message relevant to them. More detailed studies involving driver interviews downstream of the VM!3 site to determine the relevance of the message, as well as the response to it, include those by Kawashima (1991) and Durand-Raucher et al. (1993). These studies have produced more precise estimates of compliance but the results are obviously limited to those messages which were on display at the time the interviews were being conducted. A number of researchers have sought to overcome this restriction by examining response to a range of messages presented via a stated preference exercise (see for example Hato et al., 1995; Shao et al., 1995 and Bonsall and Whelm, 1995), via a route-choice-simulator (see for example Firmin, 1996; Bonsall and Merrall, 1995 ; Bonsall and Palmer, 1997) or via a full scale driving simulator or system mock-up (see for example Mast and Ballas, 1976 and Brocken and Van der Vlist, 1991). This research has suggested that response is highly dependent on message content, subjects' network knowledge, and on the extent of any implied diversion. We see particular value in extending this earlier work to consider a wider range of messages and to determine whether the route-choice-simulator results can be repeated and extended using a somewhat cheaper methodology - namely stated preference analysis. The objectives of the work reported in this paper were thus: to extend to our existing database on drivers' response to traffic information and route advice provided in variable message signs, to include a wider range of messages. to construct explanatory models of drivers' route choice behaviour in response to a variety of messages to explore the factors influencing this response to compare these results with previous results obtained using a variety of data collection methods to draw policy conclusions, where appropriate, on the use of variable message signs to influence drivers' route choice to draw conclusions, where appropriate, on our data collection and modelling methodology