Optimizing Traffic Diversion Around Bottlenecks

Transcription

1 22 Optimizing Traffi Diversion Around Bottleneks YI-CHIN HU and PAUL SCHONFELD ABSTR.CT A traffi simulation and optimization model has been developed to analyze traffi flow in large networks with severe queuing. The model an be used to evaluate the impats (e.g., travel time, operating osts, aidents, fuel onsumption, and pollutant emissions) of any assignment over time and to minimize ombinations of suh impats. The influenes on optimal assignment of traffi inflow rates and durations, relative route lengths and apaities, queue storage apaities, and other fators are shown for a simple network. A omparative analysis of route-diversion and apaity-expansion alternatives is given for the more omplex network on Maryland's Eastern Shore. A bottlenek along a highway may be defined as a relatively short setion with substantially less apaity than the rest of the road. For example, a temporary bottlenek may be aused by road repair work or an aident, whereas _a long-lasting bottlenek may be aused by any narrowing of the road (e.g., lane drops, narrow bridges) or interruptions in flow (e.g., at intersetion, railway rossings, drawbridges). Whatever the reason for the bottlenek, and however short it is, its apaity sets the limit for the total roadway apaity and degrades servie levels even before tnat apaity limit is reahed. When roadway volume v exeeds bottlenek apaity Cb, a queue would grow upstream of the bottlenek at the rate R, where For this purpose, a marosopi traffi simulation and optimization (TSAO) model was developed in a reent study (2-4). This model an simulate queu +ng upstream frrnn -bottleneks [inluding the interations of queues from various network links by using Lighthill' s shokwave funtion (_)I. The model an predit traffi impats and determine the assignment that minimizes a speifi objetive funtion (e.g., travel time or total system osts). Event-san time management was used to enhane the omputation effiieny in large network appliations. A detailed desription of this model is available elsewhere (4). Although this model an deal with large highway networks and demand distributions that are omplex over both spae and time, it is primarily used here to examine basi parameters (e.g., traffi inflow rate and duration, length and apaity of alternate routes, relative loations of bottleneks and diversion points) that influene the optimal diversion strategy in a simple network, whih is shown in Figure 1. Although this appliation grossly underuses the apabilities of the model, it permits researhers to obtain simple traffi diversion guidelines that are appliable at many loations with similar network onfigurations. A similar analysis and set of guidelines might also be developed for a family of simple network onfigurations (e.g., with more alternate routes and varying loations of diversion and reentry points). However, as network omplexity inreases, it beomes less pratial to speify general diversion guidelines and more desirable to simulate the atual. network witn its speifi harateristis. Some results of suh an appliation for the Maryland Eastern Shore network are given later in this paper. Hene the queue length at time t is (1) Bottlenek 4 lane freeway (main route) l(t) / R(t) If alternate routes around the bottleneks are available and used by motorists when volumes are high, the queuing delay osts may be onsiderably redur.eci. Snr.h rnnt.p Cliver1;1inn m>1y ot1r spontaneously. In theory (1), unrestrited motorists would hoose their routes in suh a way as to equalize travel impedane along all alternate paths that are atually used. That theory presupposes that motorists have perfet information and make optimized rational deisions. In pratie, motorists may often have little information on whih to base a rational deision, espeially if they are unfamiliar with alternate routes or if a temporary bottlenek develops downstream. Furthermore, in most networks the useroptimized traffi assignment results in higher total impedane than a system-optimized assignment determined by a entral ontroller. Hene at loations where alternate routes are available around bottleneks it is desirable to have either a set of route-diversion guidelines prepared in advane or an algorithm that an determine the optimal assignment. In either ase it should be possible to speify the fration of traffi to be assigned to various routes at various times. (2) 2 ml Diretion of Travel FIGURE 1 Base network. SIMPLE NETWORK 2 lane hlwey (elternete route) The baseline network shown in Figure 1 onsists of a main route, whih is a four-lane freeway, exept for a short bottlenek, and a two-lane alternate route. The bottlenek is a setion of two-lane rural highway, 1 mile long, with a baseline apaity of 9 vehiles per hour in the relevant diretion. The apaity of the alternate route (75 vehiles per hour) is ontrolled by the entry ramp from the main route at the diversion point. The two routes are equal in length (3 miles between the diverge and merge points), and the distane between the di-

2 Hu and Shonfeld 23 version point and the bottlenek on the main route is 9 miles. In the baseline the traffi inflow rate equals 125 perent of the total orridor apaity, and an inflow duration of 2 hr is used. Two ases were onsidered for the alternate route: 1. No opposing traffi is onsidered downstream of the ramp, whih means that vehiles an travel faster than on the rampi and 2. Heavy opposing traffi has limited the available apaity on the whole streth of the alternate route, so that the downstream set ion has the same apaity as the ramp. Beause of the opposing traffi, ase 2 provides a muh lower level of servie on the alternate route. The free-flow travel time on the alternate route is the same as on the main route in ase 1 and is 5 perent longer than on the main route in the seond ase. The objetive funtion to be optimized is a total ost funtion that onsists of the value of users' time, vehile operating osts, and aident osts. An oupany of two passengers per vehile and a value of time of $4 per passenger hour ($8 per vehile hour) were used. The onsumer prie indies of Deember 1982 were used to update the vehile oper- ating osts and aident osts from the 1977 AASHTO manual ). Sensitivity analysis <11 has demonstraed that the optimal diversion perentage does not depend substantially on values of travel time, ar oupany rates, or gasoline pries, and hene these are omitted from the fators onsidered in the following subsetions. Duration Figures 2 and 3 show the optimal perentage of traffi taking the main route for various durations of inflow and for both ases. The following observations are made. 1. The optimal fration of traffi desirable on the main route dereases sharply when the volume apaity ratio in the orridor inreases from.5 to 1 In the first ase inflow duration does not affet the optimal assignment if the orridor apaity is not exeeded. In oversaturated onditions a slight overassignment to the main route turns out to be optimal. duration has a small effet: the longer the duration, the loser the optimal as- ;.9 a:.8 Ii :I.2.7 u IL Ii ii.8.5 fration ol apaity \;>--=.:;;:;;;;;:;Ill Duration ;s 4 hours Tralll /Corridor Capaity FIGURE 2 Effets of inflow duration on optimal assignment (ase 1). :J a:. 8.: 2,7. IL Ii. ii.8.5 lratlnolratlon ol apaity Duration 1 hour 2 hours 4 hours Tralll / Corridor Capaity FIGURE 3 Effets of inflow duration on optimal assignment (ase 2)

3 24 Transportation Researh Reord 957 signment frations approah the apaity frations, as shown in Figure In ase 2, where the overall servie level on the alternate route is less than in ase 1, inflow duration affets the optimal assignment more siqnifiantly. If the inflow rate equals the orridor apaity and if the duration is as short as l hr, the optimal assignment will allow a queue to develop on the main route. As the duration inreases, the noqueue assignment beomes optimal, as shown in Figure 3. In oversaturated onditions, where traffi inflow rate exeeds orridor apaity, a small overassignment to the main route is preferable. The desirable degree of overassignment dereases as inflow duration lengthens (as in ase 1) but to a larger extent, espeially when the demand peak is short. Travel Time as t.he Objetive Funtion If travel time is the only impat to be minimized, the optimal assignments may hange slightly. Figures 4 and 5 show the minimum time assignments for ases l and 2, respetively. In general, travel time minimization favors more diversion to the alternate route than ost minimization, espeially in undersaturated onditions. If the orridor apaity is exeeded, the differenes between minimum time and minimum ost assignments beome negligible. Ne t work Configuration The relative route lengths and bottlenek loations affet optimal assignments, espeially insofar as the lengths of queue storage setions are hanged. Figure 6 shows that as the length of the alternate route inreases, the fration of the traffi staying on the main route should inrease. The effets of length variations are signifiantly larger in ase 2, where the traffi in the opposite diretion down grades the overall level of servie on the alternate route. If the alternate route length is doubled, the optimal fration on the main route inreases from.58 to.72 in ase 2, and from.55 to.64 in ase 1. If there is adequate queue storage area on the main route, it may be preferable to allow a queue to develop there. Figure 7 shows how the length of the storage setion affets the optimal assignments. In the first ase, where the alternate free-flow time on the alternate is as satisfatory as on the main route, the optimal assignment is insensitive to the loation of the bottlenek. In ase 2 the optimal assignment inreases the fration on the main route if the length of the storage setion is less than 3 miles. Beyond 3 miles, for the given inflow rate and duration, any inrease in storage will not hange the optimal assignment signifiantly. Variations in Capaities If the apaity of the bottlenek or of the alternate route is expanded, a redistribution of traffi should our to minimize system osts. In Figure 8 the 45-degree line indiates assignment ratios equal a:.11 :E. 7 -;: u.::: fration of apaity Duration 1 hour 2houro 4houre Tralll I Corridor FIGURE 4 Optimal fration for minimizing total time (ase 1) a:.s.7 :E Duration u.11 1 hour.::: Ci...5 fration of apaity on moln route hours 4 houro Trelll I Corridor Capaity FIGURE 5 Optimal fration for minimizing total time (ase 2).

4 Hu and Shonfeld 25.8 : d a ;; :II a u h..7.8 frttoa. of ep&uy on main roate O.liO 1. l.lio 2. Lonrth (A1t.)/Lon1th (main) Ratio Lo D rth of tho Alternate Route (mi) FIGURE 6 Effets of length ratio on optimal assignment.. 2 (Oppooln1 Traffi). 1 ' (Jllo Oppo1ln1 Traffi) : Oii :II a h. I..6.liO of apaity CH 2 (Oppoolnr Traffi) Caoo (Jllo Oppo1ln1 Traffi) Diltane Between Bottlenek and Diver11ion Point (mi) FIGURE 7 Effets of loation of bottlenek on optimal assignment. to the route apaity ratios. An optimal assignment above this line means an overassignment to the main route. As shown in Figure B, the lines obtained by onneting the optimal assignments for various apaity distributions are above and nearly parallel to the 45-degree line in both ases. This means that traffi should be slightly overassigned to the main route, but the degree of overassignment is insensitive to the apaity ratios. However, the degree of overassignment is larger in ase 2 than in ase 1. COMPLEX NE'IWORK In a reent study () the TSAO model was applied to the Maryland Eastern Shore network, whih is shown in Figure 9. Summer rereational traffi between the Atlanti Oean resorts and the metropolitan areas of Baltimore and Washington, D.C., reates severe ongestion on the network, espeially at two narrow bridges at Cambridge and Vienna. Capaityexpansion projets an improve the level of servie, but the demand peaks our too infrequently (15 summer weekends in this ase) to justify any largesale onstrution. Hene the TSAO model was used to analyze various alternatives for improving the quality of servie on the network, inluding bridge reonstrution, lane widening, and route diversion. The network onsists of 3 nodes and 35 links and overs an area of approximately 3, miles 2 Traffi between eight origin-destination pairs, inluding divertible through traffi and nondivertible loal traffi, was simulated, and the demands were expressed as time-varying step funtions. Periods of up to 15 hr of traffi had to be simulated. The following alternatives for improvement were analyzed: 1. Do-nothing: 2. Reonstrution and widening of Cambridge and Vienna bridges into four-lane bridges: 3. Additional left-turn lane on US-5 at MD-44; 4. Avoiding stop signs at the juntion of MD- 313 and MD-14 at Eldorado and MD-313 and MD-54 at Mardela Springs by providing right-turn ramps and aeleration lanes: 5. Additional lane in eah diretion on US-5 from the end of the Bay Bridge to Wye Mills; 6. Additional lane on MD-44 from Wye Mills to the juntion of MD-16: 7. Combination of alternatives 2, 3, and 5; 8. Combination of alternatives 3, 4, and 5; 9. Combination of alternatives 1. Optimal route diversion: 11. Combination of alternatives 12. Combination of alternatives 13. Combination of alternatives 14. Combination of alternatives 6 and 3, 4, 7 and 8 and 9 and 8; and 1: 1: 1. 1; and The present and future osts of various alternatives were determined by applying the model to the

5 26 Transportation Researh Reord /.9.8 It: ;; )? ' <\ ' ;; Fration of Capaity on Main Route FIGURE 8 Effets of apaity ratio on optimal assignment. To Jlaltlaoro Waohlnrto =Two-lne@ -- Onl Nodu LEGEND US Roato D MD Route Q DE Rn1t 1 mlleo 2 FIGURE 9 Eastern Shore network. Saliobury@ Ooan City -- appropriate network onfigurations and traffi projetions. An investment analysis was performed to determine the optimal timing of the improvements. Figure 1 shows the results of the investment analysis. The alternative with the largest equivalent uniform annual net benefit is preferable. The best two alternatives--13 and 14--inorporate route diversion and onstrution projets. The worst alternative is number 2, whih involves bridge apaity expansion only; it has negative net benefits. The analysis <1> tested the sensitivity of the results to parameters suh as interest rate and value of time, and no signifiant hange was found. The rankings of the alternatives were not signifiantly hanged and the ost-effetiveness of route diversion was not lost, even when it was assumed that motorist inflexibility prevented optimal assignment and diminished the ahievable benefits by as muh as 75 perent. CONCLUSIONS If traffi inflow exeeds total orridor apaity, queues develop upstream of bottleneks. The systemoptimized flow pattern depends on the following fators: 1. Traffi inflow rates and peaking patterns, 2. Capaities on the main and alternate routes, 3. Duration of inflow exeeding apaity, 4. Lengths of the main and alternate routes,

6 Hu and Shonfeld 27 lfi o. Ill jlq. ; ;.; 11; < 1 I. ;; =>. ;;. -1 lntorut Jlote 8% Value of time I ub br I Year FIGURE 1 Equivalent uniform annual net benefit for various alternatives (base ase). 5. Relative loations of the bottlenek and diversion point, and 6. The volume of traffi in the opposite diretion on the alternate route. Generally, it is preferable to assign slightly more traffi to the main i;oute than its apaity share in the orridor, even if the lengths on the main and alternate routes are equal. The degree of overassignment inreases with the length of the alternate route and the traffi volume in the opposite diretion. If the duration of exessive inflow is short, it is desirable to allow queuing on the main route if adequate storage is available between the diversion point and the bottlenek. As the peak period lengthens, redued overassignment to the main route is desirable. The effets of queue storage length and inflow duration beome more signifiant as the travel time on the alternate route lengthens the inrease. The problem of determining the optimal assignment beomes more ompliated if (a) time-varying traffi demand is onsidered, (b) more omplex networks with many diversion points are studied, and () loal traffi is onsidered. The TSAO model is appliable to omplex traffi flow optimization problems. It an be used to determine the timing and extent of a diversion and to provide information for evaluating and programminq improvements in a network. REFERENCES 1. J.G. Wardrop. Some Theoretial Aspets of Road Traffi Researh. Pro., Institute of Civil Engineering, Part II, Vol. 1, 1952, pp Y.C. Hu. Traffi Flow Optimization on Rural Roads. Ph.D. dissertation. University of Maryland, College Park, Aug Y.C. Hu and P. Shonfeld. Flow Optimization on Interity Road Networks. Presented at 53rd Annual Meeting of the Institute of Transportation Engineers, London, England, Aug Y.C. Hu and P. Shonfeld. Simulation and Optimization of Traffi Flow on Interity Networks. Transportation Studies Center, University of Maryland, College Park, July M.H. Lighthill and G.B. Whitham. On Kinemati Waves: A Theory of Traffi Flow on Long Crowded Roads. In HRB Speial Report 79: An Introdution to Traffi Flow Theory, HRB, National Researh Counil, Washington, D.C., 1964, pp A Manual of User Benefit Analysis of Highway and Bus Transit Improvements. AASHTO, Washington, D.C., Publiation of this paper sponsored by Committee on Freeway Operations.