A Comparison of Tram Priority at Signalized Intersections
aa r X i v : . [ n li n . C G ] N ov A Comparison of Tram Priority at SignalizedIntersections
Lele Zhang and Timothy GaroniSchool of Mathematical Science,Monash University, Victoria 3800, AustraliaTel: +61 3 9905 4503, Fax: +61 3 9905 4403,Email: [email protected]: [email protected] 2, 2018
Abstract
We study tram priority at signalized intersections using a stochas-tic cellular automaton model for multimodal traffic flow. We simulaterealistic traffic signal systems, which include signal linking and adap-tive cycle lengths and split plans, with different levels of tram priority.We find that tram priority can improve service performance in terms ofboth average travel time and travel time variability. We consider twomain types of tram priority, which we refer to as full and partial pri-ority. Full tram priority is able to guarantee service quality even whentraffic is saturated, however, it results in significant costs to other roadusers. Partial tram priority significantly reduces tram delays whilehaving limited impact on other traffic, and therefore achieves a bet-ter result in terms of the overall network performance. We also studyvariations in which the tram priority is only enforced when trams arerunning behind schedule, and we find that those variations retain al-most all of the benefit for tram operations but with reduced negativeimpact on the network.
Keywords: traffic, tram priority, cellular automata1
Introduction
To promote use of public transport, which is a key means of alleviating congestionin urban transport networks, it is important for public transport to run reliably. Oneuseful tool is to provide transit priority at signalized intersections. Transit signalpriority (TSP) has been used in practice since the 1970s. Several studies on TSPhave been undertaken previously, either via analyzing empirical data (Currie, Goh& Sarvi 2013, Furth & Muller 2000, Kimpel, Strathman, Bertini, Bender & Callas2004, van Oort & van Nes 2009) or using simulation methods (Currie, Sarvi &Young 2007, Mesbah, Sarvi, Currie & Saffarzadeh 2010, Lee, Shalaby, Greenough,Bowie & Hung 2005, He, Head & Ding 2011, Jepson & Ferreira 2000).Most of these studies focus on bus signal priority, and very few concern trams.Compared to buses, trams operating in mixed traffic have much higher impact onother road users, and vice versa. • Trams block the entire link when they stop.
For kerbside stops, which arethe most typical and common tram stops in Melbourne suburbs (Graham &Dennis 2008, Graham, Tivendale & Scott 2011), when trams stop for loadingpassengers, they block traffic not only in their own lane but also in adjacentlanes. That is to say, the capacity of the link (at the stop) drops to zero duringthe loading period. This has a more significant impact when the kerbside stopis at the approach-side of an intersection. Trams stopping at the intersectionduring a green light will result in a waste of green time. • Trams cannot change lane.
Trams are much more vulnerable to disruptionscaused by private vehicles, especially turning vehicles, because they can-not change lane. A single turning vehicle can block a straight-going trambehind it for an entire signal cycle, due to the vehicle’s need to give wayto oncoming traffic. Such events can cause significant tram delays, even inmoderate traffic conditions, unless appropriate tram priority signals are im-posed. As a result, tram priority systems usually include a clearance phase toclear turning vehicles in the tram’s path. We remark that these events are dif-ferent from the scenario of buses operating on a separate lane. In Australia,vehicles drive on the left side of the road. Bus lanes are on the left whiletram lanes are on the right, which means that even if we assume buses don’tchange lanes they are unlike to get caught behind turning vehicles becauseleft turners don’t give way. • It is comparatively difficult for early trams to stay on schedule.
If busesrun ahead of schedule, they usually wait at transit stops, where they willnot hinder other road users. However, it is impossible for trams operating2n mixed traffic to do this. Trams stopping at kerbside stops will block atleast one lane and so reduce the link capacity. Slowing down early tramsis also impractical as it leads to capacity reduction. In this paper, besidesimplementing tram priority signals, we do not consider other strategies forkeeping trams on schedule.Due to these specific peculiarities of tram behavior, studies on bus priority cannotbe directly adapted to the case of trams.This paper aims to study the effect of different levels of tram priority via con-ducting simulations on large-scale networks governed by realistic adaptive signalsystems with open boundary conditions. Simulation studies of TSP have typicallybeen limited to small-scale networks. Jepson & Ferreira (2000) studied the impactof active bus priority under various traffic conditions on a 4-lane route. Currie et al.(2007) also considered a 4-lane mixed traffic environment. He et al. (2011) eval-uated the heuristic algorithm, which deals with multiple requests of priority, on a2-intersection arterial. Lee et al. (2005) tested the advanced TSP control methodon one intersection. These studies were all confined to the question of bus priority.Furthermore, all of them, except Currie et al. (2007), in which the signal systemused was not specified, are confined to the study of fixed cycle signal systems,which are rarely used in practice nowadays.In this paper we utilize a stochastic cellular automaton (CA) model for multi-modal traffic networks, to study a number of possible tram priority schemes cur-rently used, or being considered, in Melbourne, Australia. This model was de-signed with the flexibility to allow the study of multiple vehicle types traveling inan arbitrary multimodal transport network governed by arbitrary signal systems.As we have mentioned, previous studies using microscopic simulation models fo-cused on small-scale networks, because microscopic simulations require a largeamount of input data and time consuming. This CA model is mesoscopic, in thesense that although individual vehicles are modeled, fine-grained details of indi-vidual driver behavior are treated in a course-gain, statistical, manner. The modelwas specifically designed to provide a simple and fast way to study arbitrary trafficsignal systems, on large arbitrary networks. Using this model, we study the behav-ior of four distinct types of tram priority schemes on a generic 8 by 8 square-latticenetwork governed by SCATS (Sydney Coordinated Adaptive Traffic System). Ofthese four types of tram priority, one corresponds to the method currently used bythe Melbourne’s road authority, VicRoads, while the other three are variations cur-rently being considered for trials. We study and compare the mean tram travel timeand variability produced by the different priority systems, as well as the impacton private vehicles. We also evaluate the network performance in terms of persondelays. 3dopting the classification of transit priority strategies mentioned in (Furth &Muller 2000), the four schemes considered all belong to active priority, which isto say the signal control system starts priority strategies when the trams are de-tected at prescribed locations. The scenarios can be divided into two groups: full (or absolute ) and partial priority. Signals with absolute tram priority start the pri-ority phase immediately after detecting a tram and keep the phase running untilthe tram traverses the approaching intersection. The partial priority group has lessdisruptive priority tactics, which include a clearance phase and a green extension.For both absolute and partial priority, we consider two variants: unconditional and conditional priority. Conditional priority is active only when trams are be-hind schedule. Unconditional partial priority is the system currently employed inMelbourne. Given the obvious practical importance of improving the reliabilityand efficiency of public transport, VicRoads is interested in learning under whatconditions, if any, absolute tram priority might be desirable. This was the initialmotivation for the present study.
The multimodal CA model used in our simulations extends the NetNaSch unimodaltraffic model, (see (de Gier, Garoni & Rojas 2011) for a comprehensive descrip-tion), to include multimodal traffic and complex vehicular behaviors. The modelis designed to simulate large-scale traffic networks with any number of distinct ve-hicle classes. In this paper, we focus on two vehicle classes of private vehicles (or cars ) and trams .We now summarize the details of the specific network and input parameterssimulated in the present study.
Melbourne’s tram network consists of approximately 250km of track. Of this250km, approximately 167km of the tracks occur on mixed roadways, in whichtrams and private vehicles share the same lane. The particular network we simu-lated in this study consists of a regular × square grid, illustrated in Fig. 1(a). Thisis a generic network, however, is also a good representative of typical Melbournesuburban road networks, e.g. see in Fig. 1(b). In this network, each alternatingeast-west route is a tram route. For each tram link there are two lanes, of which theright lane is a car-tram mixed lane, whereas for a non-tram link there are two lanesplus an additional right-turning lane.Each link of the model is a simple one-dimensional stochastic CA obeying (aslight generalization of) the Nagel-Schreckenberg dynamics (Nagel & Schreckenberg4 a) !!!!!!!!!!!!!!!!!! ! " ! !!!! (b) Figure 1: Left: Illustration of an 8 by 8 square-lattice network studied in our sim-ulations with each alternating east-west route being a tram route. All links carrybidirectional traffic. Boundary links are treated as ramps (buffering zones) for in-putting and outputting vehicles. Right: Google map of the network (main roadsonly) in St Kilda East and Caulfield, Melbourne, Australia.1992) with simple lane-changing rules. Each lane is discretized into a number ofcells, each of 7.5m long, corresponding to the typical space occupied by each pri-vate vehicle in a jam. Each vehicle can occupy z cells, z = 1 , , . . . , and takespeed v = 0 , , . . . , v max , depending on local traffic conditions. Trams operatingin Melbourne vary from 14m to 30m long, and they travel more slowly than privatevehicles in mixed traffic. Therefore, in our simulations, we set z = 1 and v max = 3 for private vehicles, and set z = 3 , i.e., 22.5m long, and v max = 2 for trams. Inaddition, the model includes, at each time step and for each vehicle, a random unitdeceleration which is applied with p noise . By appropriately setting p noise , we ob-tain an average free-flow speed for cars of approximately 60km/hr and for trams of45km/hr (see (de Gier et al. 2011) for details).The length of each bulk and boundary link was set to m, which correspondsto the typical distance between signalized intersections in a suburban road networkin Melbourne. The length of each right-turning lane was set to m. The modelincludes boundary links as a means of inputting and outputting vehicles, but doesnot consider them part of the network for the purposes of measuring observables. Tram Operations A , C , D , G , F and E are standard phases, and right-turning clearance phase E T and extensionphase B are tram priority phases. Phases A , C , D and G are used at non-tramnodes, whereas phases A , C , D , E and F are used at tram nodes. Dashed paths arerequired to give way to continuous paths.In actual road networks in Melbourne, a typical scenario along a tram route isthat trams operate in the right-hand lane of a two-lane link, with stops being locatedkerbside. When a tram stops to load/unload passengers, traffic in the left-hand lanemust come to a stop in order to give way to passengers. In our model, for eachtram link there are three stops, one stop every 250m, including one (approach-side)intersection stop and two mid-link stops, as illustrated in Fig. 2. In our simulations,the probability ζ s that a tram loads/unloads passengers at stop s was set to if s was an intersection stop and . otherwise. The loading/unloading time ω s at theintersection stop was sec, and sec at the mid-link stops.For each tram link in the eastbound (priority) direction, there are 2 tram detec-tors. The mid-link detector is located 60m after the second mid-link tram stop. Theend-link detector is located 7.5m back from the approaching intersection. Whena tram passes a detector, the system will register this event and then make an ap-6ropriate signal control decision. These control decisions are discussed at lengthwhen we describe traffic signal systems in the next section. In this paper we consider open boundary conditions, and so the density in the net-work is not controlled directly. Instead, at each time step, vehicles enter a bound-ary inlink with a prescribed inflow rate and exit via a boundary outlink with aprescribed outflow rate.We simulated the network over a 4-hour period, and measured the last 3 hours,considering the first hour as a burn-in period. We applied two orthogonal peakdirections: eastbound and southbound. SCATS signal coordination (linking) wasset in the eastbound direction, to establish green-wave behavior.
Private Vehicles
The inflow rate for cars follows a typical AM-peak profile, and is higher inthe second and the third hours than the other hours. The inflow rates in the peakdirections are about twice as large as those in the counter-peak directions during thepeak hours. For tram inlinks, the inflow rates of vehicles are only of those forthe non-tram inlinks in the same direction. The outflow rates have similar profilesto the inflow rates. We consider two scenarios: over-saturated (OS) and unsaturated(US). In the US scenario the network is running close to capacity. Fig. 3 shows theresulting density profiles of two typical links in the north-south direction in themiddle of the network when no tram priority system is applied. We note that theprecise density profile for each link depends on the signal systems used, the choiceof boundary conditions, and the link’s location in the network.
Tram Schedules
Trams are inserted into the network on the boundary inlinks periodically atdeterministic times. Every hour 12 trams are scheduled on each tram route in thepeak direction, and 9 trams in the counter-peak direction. The first tram starts attime 00:02:00.
To mimic origin-destination behavior without introducing the computational over-head caused by origin-destination matrices and route planning, the NetNaSch modeldemands that each cars makes a random choice about its turning decision at theapproaching intersection when it enters a link. For trams, those decisions are de-terministic as they need to follow routes.As we consider two peak directions, to match up with the biased boundaryconditions, we assumed that turning probabilities for cars are also biased. In our7 li n k den s i t y NT: OS peak dircounter−peak dir (a) OS li n k den s i t y NT: US peak dircounter−peak dir (b) US
Figure 3: Time series of densities for two links in the north-to-south (peak) and thesouth-to-east (counter-peak) directions in the middle of the network with no trampriority.simulations, each link was assigned with a probability p T of continuing straightahead, a probability p b (1 − p T ) of turning into a non-peak-direction link, and aprobability (1 − p b )(1 − p T ) of turning into a peak-direction link. The parameter p b therefore controls the level of turning bias. We used p b = 0 . in our simula-tions. The value of p T depends on the link and node type. For a tram link with noexclusive right turning lane, it is difficult to make a right-turn. In reality, cars try toavoid turning on such links. Also, cars try to avoid turning into tram routes sincethey do not want to be slowed down and/or frequently stopped by trams. Therefore,we set p T = 0 . at each non-tram node and p T = 0 . at each tram node. Each node in the network was assigned with a set of phases, shown in Fig. 2,depending on the signal system, which will be discussed in the next section.
In a given simulation, for each value of τ we have a list T (1) τ,c , T (2) τ,c , . . . , T ( m τ,c ) τ,c where m τ,c is the number (possibly zero) of cars to leave the network at time τ . T ( i ) τ,c is the total amount of time spent in the network by the i th such car. Analogously,we have a list T (1) τ,t , T (2) τ,t , . . . , T ( m τ,t ) τ,t for trams. In a simulation of duration N τ o , the total numbers ( throughputs ) of carsand trams that have traversed the network are therefore O c := N X τ = τ o m τ,c and O t := N X τ = τ o m τ,t . (1)We define the aggregated travel time per car and tram by T c : = P Nτ = τ o P m τ,c i =1 T ( i ) τ,c O c and T t := P Nτ = τ o P m τ,t i =1 T ( i ) τ,t O t (2)We also consider the travel time variability, which for trams is given by σ t := vuut O t − N X τ = τ o m τ,t X i =1 (cid:16) T ( i ) τ,t (cid:17) + O t T t ! . (3)The value of σ t measures the extent to which the travel time varies from tram totram on a particular day. Letting O ( i ) τ,c ( O ( i ) τ,t ) be the number of occupants car i (tram i ) carries, we further define the throughput of people, travel time per person andperson travel time variability by O p := N X τ = τ o m τ,c X i =1 O ( i ) τ,c + m τ,t X i =1 O ( i ) τ,t ! , (4) T p := N X τ = τ o m τ,c X i =1 O ( i ) τ,c T ( i ) τ,c + m τ,t X i =1 O ( i ) τ,t T ( i ) τ,t ! , (5) σ p := vuut O p − " N X τ = τ o m τ,c X i =1 O ( i ) τ,c (cid:16) T ( i ) τ,c (cid:17) + m τ,t X i =1 O ( i ) τ,t (cid:16) T ( i ) τ,t (cid:17) ! + O p T p . (6)In our simulations, we assumed that the number of occupants that each carcarries is identical, that is, O ( i ) τ,c = o c = 1 . (VicRoads 2013). Furthermore, weassumed that the occupancy of trams operating in the same direction is the same.Namely, O ( i ) τ,t = o t,p = 80 if the tram runs in the peak direction and otherwise O ( i ) τ,t = o t,n = 20 . We shall discuss the person performance as a function of o t,p and o t,n with a fixed ratio o t,p /o t,n = 4 . 9igure 4: Illustration of a linking subsystem. For each distinct choice of traffic signal systems and boundary conditions, we per-formed independent simulations, in order to estimate the expected values ofthe quantities defined in the last subsection. We used one standard error to set theerror bars.
The SCATS traffic signal system uses knowledge of the recent state of traffic tochoose appropriate values of three key signal parameters: cycle length, split time,and linking offset. At each intersection it can adaptively adjust both the total cyclelength, and the fraction ( split ) of the cycle given to each particular phase. In addi-tion, it can coordinate ( link ) the traffic signals of several consecutive nodes alonga predetermined route in a subsystem by introducing offsets between the startingtimes of specific phases, thereby creating a green wave. Since all of the tram prior-ity process discussed here are/would be implemented in Melbourne using SCATS,we now give a brief description on the relevant details of our model of SCATS. A subsystem is a group of nodes which all share a common cycle length. Withineach subsystem, we appoint a unique master node m , and the remaining nodesare slave nodes. The common cycle length of the subsystem is determined by themaster node based on its local traffic condition. The plot in Fig. 4 illustrates asubsystem on an east-west route, which is used in our simulation.To implement linking, each node is assigned a special phase P ∗ , which is its linked phase . The linked phase of a slave node s is coordinated to start δ sec afterthat of the master node m . Ideally, the linking offset δ should be chosen based onthe distance L between m and s , and the instantaneous local space-mean speed. Inpractice, actual implementations of SCATS tend to operate with fixed offsets duringa given period of the day (for example morning peak hour). In our simulations we10herefore used a fixed linking speed km/hr, which is just slightly less than theaverage free-flow speed of 60km/hr. In practice, SCATS chooses cycle length C based on local traffic conditions, asquantified by the Degree of Saturation (DS). If traffic is congested, signaled by alarge DS, then cycle length is increased by a fixed amount. Conversely, if greentime was wasted during the previous cycles, signaled by a small DS, cycle lengthis decreased. In our model, DS was estimated using stop-line occupancy and flowthrough the intersection. Cycle length varies from sec to sec. See Appendixfor the detailed SCATS cycle length algorithm used in our model.Once a new cycle length C ′ is determined, the new split time S ′P of phase P istaken to be proportional to S P DS P of the previous cycle: S ′P = S P DS P P P S P DS P [ C ′ − number of phases × S min − total amber time ] + S min . (7)In the case where some phases are imposed with fixed split, the above expressioncan be easily modified to choose split times for the remaining phases. An ambertime of sec is imposed for each phase-swap unless the two phases have preciselythe same set of paths, e.g. A to B . A minimum split time S min = 5 sec fornon-tram-priority phases was used in our simulations. On non-tram nodes, whose inlinks are all non-tram links, we apply the aboveSCATS model with signal linking from east to west and phases A , D , C and G in Fig. 2. For tram nodes, we consider five variants of SCATS with/without trampriority: NT . SCATS with no tram priority. PU . SCATS with partial and unconditional tram priority. PC . SCATS with partial and conditional tram priority. AU . SCATS with absolute and unconditional tram priority. AC . SCATS with absolute and conditional tram priority.11e do not apply linking along tram routes since the tram priority phase andtram loading/unloading renders the linking inefficient. Therefore tram nodes choosetheir own cycle lengths and split plans according to their local traffic conditions,independent of their neighbors. NT is the basic SCATS system for tram nodes with no tram priority. In short,it assigns of the cycle length to either phase E or F , and runs F once and E twice every cycles. Cycle length and split plan are chosen prior to the startof each cycle, which is independent of the status of trams, and are not modifiedmid-cycle. The mechanism of NT is given in Algorithm 1. Algorithm 1. NT if node n is to restart a new cycle, then Increment c (n) Choose C using Algorithm 4 if c (n)%3 = 0 , then Set S E = 20% C else Set S F = 20% C end if Choose splits for A , C and D using (7) with the remaining cycle time else Implement phases E (or F ), A , C and D in order end if *Function x % y gives the remainder from dividing x between y . The observable c (n) acts as a counter for node n , recording how many cycleshave been implemented. The purpose of phases E and F is primarily to clear right-turning cars in the east-west direction. One of them is implemented each cycle.Since the right lane is shared by trams and cars, it is difficult to obtain a goodestimate of DS in this lane. In actual practice, a fixed split is therefore imposed on E (and F ).If no tram priority process is active, then PU , PC , AU and AC behave essen-tially the same as NT . When a tram passes a mid-link detector, a priority processis called provided that no one is already running. Then priority phases are imple-mented according to the location of the tram. To simplify the exposition of thepriority process, we use variable ∆ to indicate the position of the tram that hastriggered the process: ∆ = 1 if the tram has passed the middle-link detector butnot the end-link one; ∆ = 2 if the tram has passed the end-link detector but hasnot traversed the intersection; and ∆ = 0 if the tram has traversed the intersection. PU includes two tram priority phases E T and B , and runs E T , E (or F ), A , B , C and D in order, possibly skipping E T and/or B . In short, when ∆ = 1 , PU E T to let cars, especially those turning right, traverse the intersectionand clear a passage ahead of the tram. When ∆ = 2 , PU runs phase B in order toincrease the probability that the tram traverses the intersection in the current cycle.The detailed signaling algorithm for PU when priority process is active is given inAlgorithm 2. Algorithm 2. PU if node n is to restart a new cycle, thenif phase F is to run, then Replace F with phase E end if Subtract as much as C from the nominal split time of phase C if ∆ = 1 , then Give C to phase E T and C to phase B else ( if ∆ = 2 , then )Give C to phase B end ifelseif phase E T is running and ∆ = 2 , then Terminate phase E T immediately, skip phase E and initiate phase A end ifif phase B is to start and ∆ = 1 , then Skip phase B end ifif ∆ = 0 , then Terminate (or skip) phase E T (or B ) immediately end ifif phase E T and/or B is terminated early or is skipped, then Return the unused time to phase C end ifend if PU is a partial priority system in the sense that the time for running priorityphases E T and B is limited, not more than C per cycle, and the implementationof E T and B may suffer delays. For PU the priority process can be called at anytime during a cycle, but will not take effect until the following cycle. This delaymay result in efficiency reduction of the priority process. Next we proceed to thesignal system with absolute tram priority, which has no delay or restriction on timein implementing the priority phase.Unlike PU , the AU system does not run the extension phase B . When the trampriority process is triggered, it starts phase E T immediately and keeps running it13ndefinitely until the tram that triggered the process has traversed the intersection.The detailed algorithm is given in Algorithm 3. Algorithm 3. AU Let P i be the phase that is interrupted by the priority processTerminate P i immediately provided that it has run for S min if ∆ = 0 , then Run phase E T elseif P i +1 = E , where P i +1 is the phase following P i , then Run phase F else Run P i +1 end ifend if For AU any phase may be terminated early. To avoid possible pathological DSvalues caused by the priority process, the cycle length and the split plan for nextcycle are not updated unless no phase is closed earlier than it should be. PC and AC are conditional variants of PU and AU respectively. In these cases,tram priority processes can be called only if trams are behind schedule. In orderto determine whether a tram is running on time, we assign each detector d withan expected arrival time ¯ T d . A tram is then considered to be late if its travel timewhen it arrives at the detector d is larger than ¯ T d . The expected arrival time ¯ T d iscomputed based on the location of the detector and the expected travel speed of thetram, excluding loading time. Let L d be the travel distance to the detector d and ¯ v t be the expected tram travel speed. The expected accumulated tram loading time is ¯ P d = P si =1 ζ i ω i , where i = 1 , , . . . , s are stops that the tram has passed so far and ζ i and ω i are the stopping probability and loading time at stop i . Therefore ¯ T d = L d ¯ v t + ¯ P d . We used ¯ v t = 27 km/hr in our simulations. The expected travel speedincluding loading time is then about km/hr, which is consistent with the averagetram travel time in the mixed traffic environment in Melbourne (VicRoads 2013). Fig. 5 compares the tram performance for various signal schemes. As expected,tram priority reduces the average tram travel time in the eastbound direction, whencompared to the no priority system NT , and the improvement is more significant14nder the OS scenario than US. It is also unsurprising that the AU scheme producesthe largest improvements, saving about 56% and 48% eastbound travel times underOS and US respectively. AU achieves the goal that trams traveling in the peak(priority) direction are rarely delayed, even in congested conditions. However, itresults in significant delays for westbound trams. The average travel times underthe PU system lie in-between the results of NT and AU . The performance ofeastbound trams is improved whilst westbound trams does not suffer significantdelays. The conditional systems PC and AC , compared to their unconditionalversions PU and AU separately, result in slightly longer eastbound travel times,but have less impact on the westbound direction.In terms of throughputs, the priority systems produce essentially the same re-sults. NT results in a marginally lower eastbound throughput than other systems inthe US scenario. This discrepancy increases significantly in the OS case.Bus priority only produces significant delay savings at high levels of saturation(Jepson & Ferreira 2000). By contrast, tram priority achieves great savings in bothunsaturated and over-saturated scenarios. This is because trams are more likelyto be affected by cars, especially right-turning ones. Since trams cannot changelane, a single right-turning car, which has to give way to opposite traffic on themixed traffic lane during phase A (or B ) could block the tram for an entire phaseand cause a significant delay. Therefore, tram priority plays a significant role indetermining tram performance. For NT , the large delay in eastbound tram traveltimes is due to insufficient running time for phase E (or E T ). Analogously, the AU scheme provides the largest delay in westbound travel times, because it doesnot allocate sufficient time for phase F . The partial priority schemes balance thedemands for E (or E T ) and F and give acceptable results for both directions.In addition to improve travel times and throughputs, tram priority significantlyreduces eastbound travel time variability. Similar to the travel time results, theabsolute priority systems provide the best result in the eastbound direction and theworst result in the westbound direction. In the OS scenario, the two partial priorityschemes outperform NT in both directions. Fig. 6 shows the mean travel time of cars traveling along different approaches. Forthe west-east direction, we separate cars that have traveled along non-tram routesfrom those along tram routes. We remark that a car is considered to travel alonga tram route only if it traverses the whole route without turning into other links.Similar definitions are used for cars traveling in different directions.The performance of cars traveling along tram routes is quite similar to that oftrams. Although the inflow rate of cars on tram routes is much less than that on15
T PU PC AU AC051015202530354045 signal scheme t r a m t r a v e l t i m e ( m i n ) OS W−to−E E−to−W (a) Mean tram travel time (OS)
NT PU PC AU AC051015202530354045 signal scheme t r a m t r a v e l t i m e ( m i n ) US W−to−E E−to−W (b) Mean tram travel time (US)
NT PU PC AU AC050100150 signal scheme t r a m t h r oughpu t OS W−to−E E−to−W (c) Mean tram throughput for all 4 routes(OS)
NT PU PC AU AC050100150 signal scheme t r a m t h r oughpu t US W−to−E E−to−W (d) Mean tram throughput for all 4 routes(US)
NT PU PC AU AC024681012141618 signal scheme t r a m t r a v e l t i m e de v i a t i on σ t ( m i n ) OS W−to−E E−to−W (e) Tram travel time variability (OS)
NT PU PC AU AC024681012141618 signal scheme t r a m t r a v e l t i m e de v i a t i on σ t ( m i n ) US W−to−E E−to−W (f) Tram travel time variability (US)
Figure 5: Tram performance. Error bars corresponding to one standard deviationare shown but are usually too small to observe.16
T PU PC AU AC0510152025303540 signal scheme p r i v a t e v eh i c l e t r a v e l t i m e ( m i n ) Tram route: OS
W−to−E E−to−W (a) W-E tram routes (OS)
NT PU PC AU AC0510152025303540 signal scheme p r i v a t e v eh i c l e t r a v e l t i m e ( m i n ) Tram route: US
W−to−E E−to−W (b) W-E tram routes (US)
NT PU PC AU AC0510152025 signal scheme p r i v a t e v eh i c l e t r a v e l t i m e ( m i n ) OS N−to−S S−to−N (c) N-S routes (OS)
NT PU PC AU AC0510152025 signal scheme p r i v a t e v eh i c l e t r a v e l t i m e ( m i n ) US N−to−S S−to−N (d) N-S routes (US)
NT PU PC AU AC024681012 signal scheme p r i v a t e v eh i c l e t r a v e l t i m e ( m i n ) Non−tram route: OS
W−to−E E−to−W (e) W-E non-tram routes (OS)
NT PU PC AU AC024681012 signal scheme p r i v a t e v eh i c l e t r a v e l t i m e ( m i n ) Non−tram route: US
W−to−E E−to−W (f) W-E non-tram routes (US)
Figure 6: Mean car travel times. Error bars corresponding to one standard deviationare shown but are usually too small to observe.non-tram routes, the car travel time along tram routes is much longer, which is17artly due to trams and partly due to right-turning cars at nodes. Right-turning carsresult in capacity drops at tram nodes, since there are no exclusive right-turninglanes on tram routes and such vehicles are required to give way to opposing trafficduring phases A and B and so hinder other straight-going vehicles behind them.As expected, when tram priority process is active, regardless of the schemeused, both southbound and northbound travel times increase. The higher the pri-ority imposed, the more the north-south traffic gets penalized. Even though the AU and AC schemes penalize all three non-priority directions, they penalize thenorth-south traffic more than PU and PC do. The impact on the north-south traf-fic is rather negligible when the network is unsaturated however. This is becauseSCATS uses adaptive split plans; when the congestion in the north-south directiongrows as a result of giving priority to trams, it adjusts the split plan and assignsmore split time to the north-south phase after priority process is complete. Never-theless, this adaptivity becomes less effective when the tram volume is high and/orthe tram route is over-saturated.Interestingly, we observe from Fig. 6(e) that in the OS regime tram priority canpenalize the traffic in parallel non-tram routes. Perhaps surprisingly, the penaltygenerated by PU and PC is larger than that by AU and AC . This arises becauseabsolute tram priority results in larger decreases in both the north-south flow andthe amount of traffic turning into the east-west direction, which therefore inducesan effective gating of the west-east non-tram routes. This type of unexpected non-local behavior illustrates the importance of studying the response of the network asa whole, rather than just focusing on the route on which priority is being imposed.Finally, we note that the reason the mean travel time along the eastbound non-tramroutes is always less than that along the southbound routes, both of them are peakdirections, is simply a consequence of signal linking being applied in the eastbounddirection. One aim of traffic management for road authorities is to move as many people aspossible in each lane in order to maximize the use of road. Compared to privatevehicles, trams have higher occupancy levels, which is a key motivation of trampriority. In this subsection we address a quantitative question, which is what tramoccupancy is to justify various tram priority levels in different scenarios. Specifi-cally, We pinned the car occupancy o c and the ratio o t,p /o t,n of tram occupancy inthe peak and counter-peak directions, and studied people travel time and through-put as a measure of network performance with various o t,p .Figs. 7(a)-(d) give the average person travel time and throughput of the wholenetwork as o t,p varies. The differences in person throughputs between the various18 t,p pe r s on t r a v e l t i m e ( m i n ) OS, fixed o t,p /o t,n = 4 NT PU PC AU AC (a) Mean person travel time (OS)
40 60 80 100 120 140 160 180 20011.51212.51313.51414.51515.5 o t,p pe r s on t r a v e l t i m e ( m i n ) US, fixed o t,p /o t,n = 4 NT PU PC AU AC (b) Mean person travel time (US)
40 60 80 100 120 140 160 180 2001.251.31.351.41.451.51.551.6x 10 o t,p pe r s on t h r oughpu t OS, fixed o t,p /o t,n = 4 NT PU PC AU AC (c) Mean person throughput (OS)
40 60 80 100 120 140 160 180 2001.11.151.21.251.31.351.41.45x 10 o t,p pe r s on t h r oughpu t US, fixed o t,p /o t,n = 4 NT PU PC AU AC (d) Mean person throughput (US)
NT PU PC AU AC02468101214 signal scheme pe r s on t r a v e l t i m e de v i a t i on σ p ( m i n ) OS (e) Person travel time variability (OS) NT PU PC AU AC02468101214 signal scheme pe r s on t r a v e l t i m e de v i a t i on σ p ( m i n ) US (f) Person travel time variability (US) Figure 7: Person performance. (a)-(d): o t,p /o t,n = 4 and o t,p = 40 , , . . . , .(e) and (f): o t,p = 80 and o t,n = 20 . Error bars corresponding to one standarddeviation are shown but are usually smaller than the symbol size of the data point.19ystems are very limited. In short, AU provides the worst result in the US case andfor o t,p ≥ in the OS case, whereas PC always provides the best result in bothcases. Next we focus on the result of person travel times.For the unsaturated network, regardless of the tram occupancy, all the priorityschemes result in reduced person travel times. The improvement is more pro-nounced when o t,p is larger, as expected. AU outperforms AC and PC when o t,p ≥ . This implies that from the perspective of individual travelers, im-plementing tram priority processes in this case improves tram performance to anextent which overweighs the negative impact on other traffic, and overall it has apositive effect on the network. We expect the crossing point determining when theabsolute priority becomes the optimal scheme should move to lower occupancyas we decrease the congestion. This is because for low congestion the signals areadaptive enough to cope with the penalties caused by tram priority.In the saturated scenario, PU and PC obtain the smallest travel times for allreasonable values of tram occupancy. The travel time curve for NT intersects with AC and AU at o t,p = 100 and o t,p = 120 separately. This implies that although theabsolute tram priority schemes bring relatively large penalties to other road users,compared to no priority scheme, they provide better overall network efficiency interms of person travel times when tram occupancy is sufficiently high.With respect to the relation between conditional and unconditional schemes,we see that the variability for PU and PC is almost identical in both traffic con-ditions, yet travel times and throughputs for PC are marginally better. Combiningthis with the results in Figs. 5 and 6, it appears that PC obtains most of the ben-efit obtained by PU but with a slightly lower penalty on the network, and there-fore arguably produces an overall better result. By contrast, compared with AU , AC unambiguously performs better in terms of person travel times, variability andthroughputs, and should be therefore preferred. We have utilized a multimodal traffic model to study a variety of tram priorityschemes in a mixed traffic environment on a square lattice network. In particularwe have studied the adaptive traffic signal system SCATS with a number of trampriority scenarios, using a morning-peak traffic profile and two orthogonal peak di-rections. We have considered two scenarios with low and high levels of saturation.Tram priority is an effective strategy to improve tram performance in terms ofboth travel time and variability. Regardless of the traffic condition, the absolutetram priority results in the best tram service in the priority direction at the expenseof delaying other traffic in the non-priority directions. At a lower level of satura-20ion, the impact of tram priority on the orthogonal direction is almost negligible,which can be explained by the adaptivity of the traffic signal system. In this case,with high tram occupancy the absolute tram priority might be justified. As thenetwork becomes more saturated however, other road users suffer more from thedisruptions caused by tram priority processes, especially the absolute tram priority.With respect to the overall person performance, the partial priority gives thebest result. In general the partial priority should be recommended. The savings forpriority-direction traffic derived from the absolute priority is negated by the costsimposed on opposing traffic, unless trams have extremely high occupancy. Foreither the absolute priority or the partial priority, the conditional version achievesalmost the same level of improvement of service as the unconditional version butwith reduced impact on other traffic. Therefore, the partial conditional prioritysystem appears worth trialling. In the case that the absolute tram priority is neces-sary, e.g. in order to keep tram service on time regardless of the traffic condition,the absolute conditional priority should be implemented, rather than the absoluteunconditional.The analysis of tram priority presented in this paper is just a first attempt atusing the multimodal traffic simulation model on large-scale networks. Futurework will extend the study of the tram priority to two directions: both peak andcounter-peak for all the priority schemes. This is challenging since counter-peak-direction tram priority may disadvantage peak-direction trams. We also intend tostudy advanced priority schemes for intersecting tram routes. In addition we havemade some assumptions to calibrate the model, including constant linking offset,constant expected tram travel speed and fixed frequency of phases E and F . Inpractice, those could depend on traffic conditions. Future work will consider theimpact of those parameters. We gratefully acknowledge the financial support of the Roads Corporation of Vic-toria (VicRoads), and we thank VicRoads staff, in particular Adrian George, An-drew Wall, Anthony Fitts, Hoan Ngo and Chris Eer for numerous valuable discus-sions. This work was supported under the Australian Research Council’s LinkageProjects funding scheme (project number LP120100258), and T.G. is the recipientof an Australian Research Council Future Fellowship (project number FT100100494).This research was undertaken with the assistance of resources provided at theNCI National Computational Merit Allocation Scheme supported by the AustralianGovernment. We also greatly acknowledge access to the computational facilitiesprovided by the Monash Sun Grid. 21 eferences
Currie, G., Goh, K. & Sarvi, M. (2013). An analytical approach to measuringthe impacts of transit priority, , Washington, DC.Currie, G., Sarvi, M. & Young, B. (2007). A new approach to evaluating on-road public transport priority projects: balancing the demand for limited road-space,
Transportation .de Gier, J., Garoni, T. & Rojas, O. (2011). Traffic flow on realistic road networkswith adaptive traffic lights, Journal of Statistical Mechanics: Theory and Ex-periment .Furth, P. & Muller, T. (2000). Conditional bus priority at signalized intersections, Transportation Research Record .Graham, C. & Dennis, C. (2008). Transforming city streets with sustainable trans-port infrastructure: Melbourne streetcar regeneration,
Transportation Re-search Board 87th Annual Meeting .Graham, C., Tivendale, K. & Scott, R. (2011). Safety at cerbside tram stops -accident analysis and mitigation,
Transportation Research Board 90th AnnualMeeting .He, Q., Head, K. L. & Ding, J. (2011). Heuristic algorithm for priority traffic signalcontrol,
Transportation Research Board 90th Annual Meeting , Vol. 2259.Jepson, D. & Ferreira, L. (2000). Assessing travel time impacts of measures toenhance bus operations. part 2: Study methodology and main findings,
Road& Transport Research .Kimpel, T., Strathman, J., Bertini, R. L., Bender, P. & Callas, S. (2004). Analysis oftransit priority using archived trimet bus dispatch system data, TransportationResearch Board 82nd Annual Meeting , Vol. 1925.Lee, J., Shalaby, A., Greenough, J., Bowie, M. & Hung, S. (2005). Advanced tran-sit signal priority control with online microsimulation-based transit predictionmodel,
Transportation Research Board 84th Annual Meeting , Vol. 1925.Mesbah, M., Sarvi, M., Currie, G. & Saffarzadeh, M. (2010). Policy-making toolfor optimization of transit priority lanes in urban network,
TransportationResearch Board 89th Annual Meeting , Vol. 2197.22agel, K. & Schreckenberg, M. (1992). A cellular automaton model for freewaytraffic,
J. Physique I France .van Oort, N. & van Nes, R. (2009). Control of public transportation operationsto improve reliability, Transportation Research Board 88th Annual Meeting ,Vol. 2112.VicRoads (2013). Traffic monitor 2011-2012, T echnical report. A SCATS – Cycle Length Decision
Every time a master node is about to restart its cycle, the cycle length is adjustedadaptively based on recent measured values of the DS. In our model of SCATS, theDS of in-lane λ and phase P is defined to be DS λ, P = 1 S P " S P − S P X t =1 (1 − o λ ( t )) + N λ S P X t =1 F λ ( t ) , (8)where o λ ( t ) and F λ ( t ) are the stop-line occupancy and flow through the intersec-tion of lane λ at time t respectively, and S P is the split time of P . The quantity N λ denotes a fixed benchmark of the time required to traverse the gap betweenvehicles at maximum flow F max .The DS of a master node, m , is given by DS m = DS P ∗ = max λ ∗ DS λ ∗ , P ∗ , (9)where the maximum is taken over all in-lanes in the linked direction during linkedphase P ∗ .For a non-subsystem node, n , the DS is defined by the maximum DS over allin-lanes and phases, DS n = max P DS P = max P max λ DS λ, P . (10)We remark that an in-lane is excluded from the computation of DS if it belongs toany of the dashed paths shown in Fig. 2, to avoid pathological DS values inducedby turning vehicles.At a given time, the weighted DS of the previous 3 cycles is defined to be wDS = 45%DS + 33%DS − + 22%DS − , (11)where DS − i is the DS of the i th last cycle.The strategy for adapting the cycle length C based on V = DS × F max andw DS , of a master (or non-subsystem) node is as follows.23 lgorithm 4. SCATS cycle length decision
Case 1: if C = C MIN & V > . , then C = C STOPPER
Case 2: if C = C STOPPER & V < . , then C = C MIN