Study On Morning Commute Problem Considering Variable Capacity And Parking Space Constraint

Traffic congestion is a kind of urban disease,which greatly affects the development of society and economy,as well as the process of urbanization.Urban traffic congestion is ususally worst during rush hour.Therefore,it is of grat significance to investigate commute problem of the peak hour.This paper study the morning rush hour commute problem,and introduce the bottleneck capacity variability and pariking space constraint into the classical Vickrey's bottleneck model.The main work is as follow:In the practical traffic system,congestion often results in long queue length.In order to alleviatie congestion,traffic management department may take some mearsures to increase the capacity of bottleneck.Motivated by this fact,we improve the traditional bottleneck model to a bottleneck model whose capacity is affected by queue length.In queue-length-dependent bottleneck model,the bottleneck capacity increases from si to s2 as the queue length exceeds a threshold D1 and decreases back to si as the queue length reduces and becomes smaller than another threshold D2(D2?D1).It has been found that multiple equilibria exist when D2<Dj.Their stability has been preliminarily studied via the day-to-day dynamics,and we found it is likely that only the equilibrium state with the lowest cost is stable against large disturbances.In the case where D2=D1,there is no multiple user equilibrium state,and the capacity does not change more than twice.Moreover,there exists a parameter range in which there is no solution unless the bottleneck capacity can switch back and forth instantaneously.The policy of opening the shoulder lane on a 2-lane highway is discussed as an application example in the final.Secondly,based on the above model,the restraint effect of public parking space is considered.As all parking spots are public ones for which commuters have to compete on a first-come-first-served basis,and the number of parking spots are limited,some commuters should take public transportation.Under this constraint,there is an interior equilibrium at which both auto and public mode are used for commuting.The number of auto commuters in the interior equilibrium denote the maximum of potential auto commuter number.Only when total parking spots number is less than the maximum of potential auto number,the parking spots play a restraining role.Although considering the parking space constraint,in the case where D2=D1,there is no multiple user equilibrium state,and the capacity does not change more than twice.Finally,this paper extents the parking space constraint to the situation where there are two kinds of parking spaces:public parking space and reserved parking space.In this situation,some commuters reserve parking spots in advance,while others have to compete for public ones or choose public transportation.In the bottleneck model with both public and reserved parking space constraint,when the total number of parking spots is larger than the potential number of commuters willing to drive themselves,commuters with reserved parking spots do not have any advantages over commuters competing for public ones,and they could mix with each other.In contrast,if the total number of parking spots is less than the potential auto commuter number,commuters competing for public spots have to commute before others who reserve parking space.Moreover,the former has a larger travel cost than the latter.In this bottleneck model,the capacity can change up to four times,but there is still no multiple user equilibrium state.In the last,we analyze the influence of the queueing length threshold,the total number of parking spaces and the proportion of parking space on the total travel cost of the system through several examples.It is found that both an appropriate parking space number and a proper combination of reserved and unreserved parking spots can eff'ectively reduce the total system cost.Because the former can increase the number of commuters using public transport,and the latter compel commuters without reserved parking spots to leave home earlier to secure public parking spots.Considering potential risk,the queuing length threshold is n o longer the smaller the better,but should be determined by the overall situation of the system.