Unsignalized Intersections

CTC-340

Hmwk

• At end of powerpoint

• STOP & YIELD controlled

• Include TWSC, AWSC and Roundabouts

• All models are based on a gap acceptance model

Gap Acceptance

• Gap – distance between back of veh and front of next veh – not headway– Each gap can allow at least 1 veh to move– Vehicle using gap is based on a rank order– Figure next slide– Rank 1 – 2,3,5,6,15,16– Rank 2 – 1,4,13,14,9,12– Rank 3 - 8,11– Rank 4 – 7,10– Why this ranking?

Rank order

Conflicting Volume

– Each movement must content with a different group of conflicting flows

– Figure next slide– Look at footnotes

• RT from major street do not conflict but some are counted in conflicting volume

• 2 stage gap acceptance – median or TWLTL present – cars can cross 1 direction of traffic at a time

Conflicting Volume

– Each movement must content with a different group of conflicting flows

– Critical volume cmx = cpxpvippj– cpx= potential movement capacity

– pvi= probability that impeding veh movement j will not block flow (impedance factor)

– ppj= probability that impeding ped movement j will not block flow (impedance factor)

Critical Gap

• Minimum average acceptable gap that allows entry for 1 turning movement– Any gap smaller than critical gap is not used

• Follow up time – minimum average acceptable time for a second queued vehicle to use a gap large enough to admit 2+ vehicles

Critical Gap

– Critical Gap • tcx = tcb + tcHVPHV + tcGG – tcT – t3LT

– Follow up time• tfx = tfb +tfHVPHV

• tcb = base critical gap, T23.2

• tcHV= critical gap adjustment for HV

• PHV= percent HV

• tcG= critical gap adjustment for grade

• tcT = critical gap adjustment for 2 stage gap acceptance

• t3LT = critical gap adjustment for intersection geo

• tfb = base follow up time, T 23.2

Potential Capacity

• Assumes that all available gaps are used by subject movement– No higher priority movements will be at

intersection– Assumes movement operates in exclusive

lane• cpx = vcx[(e^-(vcx*tcx/3600))/(1-e^-(vcx*tfx/3600))]

• vcx = conflicting flow for movement x

Impedance Effects

– Effects due to higher ranked movements using a gap• Reduces the available gaps for the subject movement• Figure next page

– First find movement capacity• cmx = cpxpvippj

• cmx = movement capacity

• cpx = potential capacity

• pvi = probability that movement i is not blocking subject flow

• ppj = probability that pedestrian movement j is not blocking subject flow

Impedance Effects

– Effects due to higher ranked movements using a gap• Reduces the available gaps for the subject movement

Impedance Effects

• pvi = 1 – vi/cmi

• vi = demand flow for impeding movement i

• cmi = movement capacity for impeding movement i

• The lower the v/c ratio for the impeding movement – the more likely that the subject flow will not be impeded

• Rank 4 movements are impeded by many movements- may end up double counting impedance factor

• p” = Pv1*Pv4*PvTH

Impedance Effects

• p’ = 0.65p” – (p”/(p”+3) + 0.6SQRT(p”)• p’” = unadjusted impedance factor• p’ = adjusted impedance factor

– Need to modify Major St LT when in shared lane • P*v1/4 = 1 – ((1-Pv1/4)/(1-(vmTH/smTH + vmRT/smRT)))

– Ped impedance factor• ppj = 1 – (vj(w/Sp)/3600)

• vj = ped flow rate

• w = lane width

• Sp= ped speed fps

Shared Lane Cap

• Movement capacities assume exclusive lanes for each movement– When movements operate out of a shared

lane• cSH = vy/vy/cmy)

• Capacity = total flow rate/ cSH

Upstream Signals

• Gap acceptance assume random arrivals for all vehicles– If signalized intersections within ¼ mile – not

true• Each platoon gives a different conflicting flow to

the downstream intersection• Very complex

2 stage gap acceptance

• Occurs at divided highways or TWLTL

• Increases capacity for minor street movements due to ability to cross 1 traffic stream at a time.

• Limiting factors are the # of vehicles that can be in the median at the same time

Flared Lanes

• Lane operates between exclusive lane and shared lane – Need to know average queue length of RT

traffic– If max queue length <= # of flared spaces –

operates like a separate lane – If max queue > # of flared spaces then

capacity is a constrained

Delay

• What is it

• Control delay – includes time stopped in queue + time to decel + accel

• Geometric delay – delay due to decel/accel to get thru intersection

• HCM uses control delay as its MOE– dx = 3600/cmx +900T((vx/cmx-1)+SQRT((vx/cmx-

1)^2 + (3600/cmx)(vx/cmx)/450T)) + 5

Delay

• Delay is given for approach lane groups– Each exclusive lane or each shared lane– Major St LT – Major street thru assumed to have no delay

• Depends on whether LT has an exclusive lane• Usually very small if it does occur

Queue Length

– Q95x = 3600/cmx +900T((vx/cmx-1)+ SQRT((vx/cmx-1)^2 + (3600/cmx)(vx/cmx)/150T)) *(cmx/3600)

– 95th percentile queue– Gives a sense of congestion at intersection– Higher queue means lower LOS

AWSC

• Based on FIFO queue– Looks at probability of intersection in a certain

condition – Determines the probability of each condition

occurring given volumes and assesses the impact

– Each approach affects the others– Iterative process

Roundabouts

– Roundabouts must be Yield controlled and have a splitter island

Example 1

A

B

35’

40’

Spd lmt = 35 mph for A45mph for B

Example 2

Homework

• Prob 23-2 Determine the potential capacities for movements 1,7,8,9

• Prob 23-3 Determine the movement capacities for movements 1,7,8,9

• Prob 23-4 Determine the shared lane capacities for movements 7,8