Abstract
Pedestrian overflow causes queuing delay and in turn, is controlled by the capacity of a facility. Flow control or blocking control takes action to avoid queues from building up to extreme values. Thus, in this paper, the problem of pedestrian flow control in open outdoor walking facilities in equilibrium condition is investigated using M/M/c/K queuing models. State dependent service rate based on speed and density relationship is utilized. The effective rate of the Poisson arrival process to the facility is determined so as there is no overflow of pedestrians. In addition, the use of the state dependent queuing models to the design of the facilities and the effect of pedestrian personal capacity on the design and the traffic congestion are discussed. The study does not validate the sustainability of adaptation of Western design codes for the pedestrian facilities in the countries like Bangladesh.
Highlights
Flow control is one of the common means to ensure proper quality of service with limited facilities in transportation and communication industry
Pedestrians usually travel at a maximum density of 1.55 ped./m2, whereas pedestrian free flow speeds start to decline at a density of 0.6 ped./m2 and ‘usual jam’ occurs at densities of about 3.32 ped./m2 [4,17,18]
We have utilized the realistic relationships among the pedestrian traffic flow variables to formulate a credible analytical model based on M/M/c/K state-dependent queuing system
Summary
Flow control is one of the common means to ensure proper quality of service with limited facilities in transportation and communication industry. The opportunity to find an appropriate analytical tool is very limited as few real-world situations conform to the requisite assumptions This causes it difficult for operators to sharply respond to the changes in traffic conditions and for planners to provide effective design for the capacity of the facilities in transportation and communication industry. To overcome some limitations and to incorporate some important determinants and functional factors, as mentioned and thereafter, in this study we will use the M/M/c/K state-dependent queuing models to control pedestrian flows and capacity based design of pedestrian facilities in open outdoor walking environment e.g. sidewalks. The M/M/s system based congestion models as derived in Eq 1 based on the model developed by Rahman et al [18] (which has been empirically validated based on the data on the pedestrian characteristics on some sidewalks in Dhaka, Bangladesh), and M/M/c/K statedependent pedestrian flow models, as formulated in Section 3, could triumph over these shortcomings to study the pedestrian movements and flow control on sidewalk facilities, and designing of such facilities
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