Chapter 8, Problem 18P

To determine

Effect on cycle length due to higher pedestrian flow rates.

Answer to Problem 18P

Cycle length value increases with , from to .

Explanation of Solution

Given data:

Calculation:

Evaluating equivalent hourly flow −

  

Similarly, evaluating equivalent hourly flow for all traffic movements −

Table 1

Approach (width)	N (56ft)	S (56ft)	E (68ft)	W (68ft)
Left turn	133/0.95 = 140	73/0.95 = 77	168/0.95 = 177	134/0.95 = 142
Through movement	443	393	593	544
Right turn	148	143	178	188
Conflicting pedestrian volume	948	1264	1264	948

Assuming lane configuration as one dedicated left turn and combined through and right lane −

Table 2

Approach	N	S	E	W
Left	140	77	177	142
Through + Right	589 (442+147)	535 (393+178)	771 (593+178)	730 (543+187)

Assume a phase scheme and find critical ratios( ) and sum of critical ratios ( ). Assuming phase as follows −

Table 3

-	Phase lE-W (Left)	Phase llE-W (Through)	Phase lllN-S (Left)	Phase lVN-S (Through)
	177	771	140	589
	1000	3000 (1600+1400)	1000	3000 (1600+1400)
	0.177	0.257	0.140	0.196

Sum of critical ratios −

  

Assuming lost time per phase ( )=

So, Total lost time −

  

Now, determining the optimum cycle length −

  

(Cycle lengths are generally multiple of , Hence OK)

Finding Total effective green time −

  

Effective time for phase can be calculated as −

  

For Phase l

  

(Assuming yellow time as )

  

For Phase ll

  

  

For Phase lll

  

  

For Phase lV

  

  

Table 4

Phase	Allocated green & yellow time (in sec)

Total cycle length

  

Green time required for pedestrian crossing can be calculated as following formula:

(Assuming the crosswalk width as < ).

  

Where,

   = cross walk length

   = pedestrian speed (assuming as )

   = number pedestrians crossing during an interval =

   = pedestrian flow rate in the subject crossing for travel direction

   = total cycle length

Calculating for each direction:

   for N direction =

   for S direction =

   for E direction =

   for W direction =

Calculating minimum time required ( ) for each approach:

Minimum time required for N approach ( ):

Minimum time required for S approach ( ):

Minimum time required for E approach ( ):

Minimum time required for W approach ( ):

Table 5

Phase	Minimum green time (in sec)

   is greater than so the allocated green and yellow time for phase is from the table 5 sec.

Sum of green and yellow time is given by,

  

Total cycle length is given by,

  

Now increasing the pedestrian volume with and calculating the minimum time required by pedestrian for each approach:

  

Table 6

New conflicting pedestrian volume

1138

1517

1517

1138

According to the new pedestrian volume calculating minimum time required by pedestrian for each approach:

Calculating for each direction:

   for N direction =

   for S direction =

   for E direction =

   for W direction =

Calculating new minimum time required ( ) for each approach:

Minimum time required for N approach ( )=

Minimum time required for S approach ( ) =

Minimum time required for E approach ( ) =

Minimum time required for W approach ( ) =

Comparing the values with table 4, and selecting new values as shown in table below:

Selecting greater values in between both and , which is taken as new minimum green time:

Table 7

Phase	New minimum green time (in sec)

Sum of green and yellow time is given by,

  

Total new cycle length is given by,

  

Conclusion:

With using pedestrian volume flow rate higher than given, cycle length increases by .