Fleet size estimation for spreading operation considering road geometry, weather and traffic

Journal of Traffic and Transportation Engineering(English Edition)

2014,1 (1 ) : 1-12

Fleet size estimation for spreading operation considering road geometry, weather and traffic

Steven I-Jy Chien':":", Shengyan Gaol, Jay N. Meegoda", Taha F. Marhaba' 1

Department of Civil & Environmental Engineering, New Jersey Institute of Technology, Newark, NJ, USA 2

School of Automobile, Chang'an University, Xi'an , Shaanxi , China

Abstract: Extreme weather conditionst i. e. snow storm) in winter time have caused significant travel disruptions and increased delay and traffic accidents. Snow plowing and salt spreading are the most common counter-measures for making our roads safer for motorists. To assist highway maintenance authorities with better planning and allocation of winter maintenance resources, this study introduces an analytical model to estimate the required number of trucks for spreading operation subjective to pre-specified service time constraints considering road geometry, weather and traffic. The complexity of the research problem lies in dealing with heterogeneous road geometry of road sections, truck capacities, spreading patterns, and traffic speeds under different weather conditions and time periods of an event. The proposed model is applied to two maintenance yards with seven road sections in New Jersey (USA), which demonstrates itself fairly practical to be implemented, considering diverse operational conditions. Key words: fleet size; road geometry; road network; spreading operation; traffic speed; winter road maintenance

1

Introduction

Weather is the second largest cause of non-recurring congestion (Rall 2010), which accounts for 25 percent of all delays. According to a report sponsored by the Federal Highway Administration (FHWA 2009), near 1 billion hours are lost each year due to weather-related delays. Icy and snowy road conditions greatly influence the road safety

(Andrey 2010) as well as temporal and spatial variations of traffic volumes (Datla et al. 2008), Spreading of chemicals and abrasives on the road network is a key operation to keep roads for safe passage. During salt spreading a wide array of resources will be utilized to ensure the best possible road condition during/after each snow storm. Early research in this field focused on the guidance on anti-icing practices ( FHWA 1995) which

• Corresponding author: Steven I-J y Chien. PhD. Professor. E-mail: chien@adm. njit. edu.

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2 can be employed under various combinations of conditions in precipitations, pavement temperatures, traffic volumes, and mandated levels of service. A guideline was developed based upon a 4-year anti-icing field test conducted by 15 state highway agencies. Recently, under the mounting pressure of high demand for improving winter road safety and mobility subject to budget constraints, it is imperative for transportation agencies to pursue the most cost-effective usage of their resources. Hence, a sound spreading model is desirable to determine fleet size (i , e. number of spreading trucks) for maintaining designated road sections/network within a given time period considering weather and traffic. The aim of this research is to develop a model which can be applied in estimating fleet size for salt spreading operation. The proposed model can be practically applied to determine the number of trucks needed for transportation agencies before the start of a snow season, considering the worst case situation including weather and geometry conditions and the corresponding traffic speed. Alternative, the proposed model can be employed to calculate the required number of spreading trucks to call out subject to forecasted weather and expected traffic. The complexity of the proposed spreading model lies in three aspects: (1) Heterogeneous road geometry and spreading patterns. A transportation agency may be responsible for a large scale network with various types of roadways Ci. e. urban vs. rural. freeway vs. arterials); as a result, the pavement width/number of lanes of each road section is a variable. (2)Variable operating speed. A time varying and location dependent speed matrix is required to determine the operating of winter road maintenance operations subject to different weathers and traffics and a cycle time (or called service time) constraint. (3) Mixed types of spreading trucks. Mixed types of spreading trucks with different capacities may be used during the spreading operations. The proposed model will address all the above

Steven I-Jy Chien et al.

issues while estimating truck fleet size for pre-assigned road sections, considering geometric properties of the pavements and ramps (i. e. lane mile, centerline mile, lane number. ramp length and length of acceleration/deceleration lanes), spreading patterns, traffic and weather conditions. and mixed types of truck fleets Ci. e. 2. 5Ton, 6-Ton, and 10-Ton trucks). 2

Literature review

Previous studies on salt spreading operation have focused on routing maintenance vehicles for a designated road network, and the objectives are to minimize the total distance traveled and fleet size. subject to operational constraints (Perrier et al. 2007; 2010). The fleet size needed for a large network was determined by road geometric condition. while traffic conditions were not considered. Considering more realistic information (i , e. the joint effect of weather. traffic and geometric conditions). a more complicated model is desirable. Muyldermans et al. (2002) estimated the fleet size based on the total load of a district divided by vehicle capacity in the districting problem. which involves the partitioning of the road network into districts to facilitate the organization of the spreading operations. The total load of a district is the total route length to be treated, and the vehicle capacity is the length that can be serviced by one fully loaded truck. However. factors influencing the fleet size estimation were ignored. including different spreading patterns and the service time constraint. It was realized that required number of spreading truck is also affected by the spreading patterns. For two road sections with same lane miles. the road section with small centerline mile may take less time than that for the road section with long centerline miles. Spreading pattern is mainly dictated by the type of highway and number of lanes. On a four lane undivided roadway. the passing lane in either direction may be spread simultaneously from the adjacent travel lane (Cifelli et al. 1979). Belt speed. spinner speed

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3

Journal of Traffic and Transportation EngineeringCEnglish Edition)

and vehicle position need not be changed since the normal spreading pattern on this type roadway is achieved by spreading simultaneously on two lanes during the singular directional pass of the spreading unit. However, the spreading patterns for other multilane highways were not clearly defined. Another issue that needs attention is the traffic speed while estimating the fleet size. During the spreading, the spreading truck speed is often impeded by traffic speed due to the adverse weather condition. Significant research efforts have been devoted to understanding the effects of weather conditions on traffic speed. Liang et al. (1998) studied the impact of fog and snow events on a section of a rural interstate freeway in Idaho. They found that the reductions in average speed were 7. 6 and 18. 13 percent for fog and snow events, respectively, comparing to that on sunny days. Daniel and Chien (2009) investigated the impact of adverse weather on traffic speeds on New Jersey roadways under a variety of weather and light conditions. It was found that under snowy condition the average traffic speed decreased between 9.3 km/h (5. 8 m/h or 15 %) to 54 km/h 03.8 m/h or 50%). A weather module was also developed as a part of FHWA's Traffic Analysis Tools (TAT) program to guide traffic engineers and transportation operations managers in analyzing and modeling weather impacts on highway traffic movements (FHWA 2010). Similarly, according to a scanning study of Japan to investigate advanced technologies for winter maintenance operations and implementation (FHWA 20(3). expressways in Japan employed variable speed limit signs in response to different road weather conditions, such as wind speed, visibility, air and road surface temperature. Agrawal et al. (2005) quantified the impact of snow and pavement surface conditions on freeway traffic flow in Twin Cities, Iowa. Four different levels of snowfall intensities are employed in the research: trace « 1. 27 mm/h), light (1. 52-2.54 mm/Ii) , moderate (2.8-12. 7 mm/h) and heavy C> 12. 7 mrri/h) . The speed reduction associated

with the four-level snow intensities are 3%-5%, 7%-9%,8%-10% and 11%-15%. Moreover, past

studies also suggested that the decrease or increase in speed variation during snow storms is influenced by road and vehicle types (Liang et al. 1998; Hanbali 1994). For instance, Hanbali (1994) found that snowy/icy conditions are associated with an average 18% and 42% speed reduction on two-lane highways and 13% to 22% reduction on freeways (more reduction on lower level of road), respectively. In addition, Chien et a1. (2001 ; 20(2) found that the primary causes of speed reduction are excessive roadway congestion, as one would find during peak travel periods, and event-induced impairment to driving conditions due to poor visibility and treacherous roadway surfaces. This finding is consistent with the observation by Shahdah et a1. (2010) that winter road maintenance aiming at achieving bare pavement conditions during heavy snowfall could reduce the total highway traffic delay up to 36%, depending on the level of traffic demand. Similarly, FHWA (2006; 2010; 2(12) has dedicated many efforts attempting to establish relationship between weather involving rates of precipitation and surface conditions and traffic flow variables. However, limited research was conducted on correlating the weather and traffic speed for specific roadway types during different time periods. In addition, during spreading operation multiple types of spreading trucks with different capacities can be employed. Considering the operation with multiple truck types, the lane-mile spread per truck by type was defined as the capacity of the truck divided by the spreading rate (Cifelli et al. 1979). Hence, the required number of trucks by type can be calculated based on the total spreading lane miles divided by the lane-mile spread per truck. However, the service time constraint for spreading on the designated road network was not considered. In summary, the proposed model and methods developed in this study can be applied to estimating the fleet size for spreading operation, in which the complexity in dealing with road geome-

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"

Steven I-Jy Chie n et al ,

tr y . wea th er a nd tra f fi c co nd it io n i di cu se d . A 'p ee d matrix . con id e r ing highwa y type . sn o w

road . (2) T h e prca din g pattern depen d s on t h e num-

in tc ns iti e • a nd ti me of a d ay . is d e veloped based

be r o f lane

o n dat a co llected fro m tran portat ion ag enci es.

and fo ur -la ne highway ( o ne- la ne two -wa y a nd

C la ru . a nd I RIX.

two-la ne two-way . re spec t ive ly ) , th e roa d ca n be

3

of a road secti o n . Fo r th e two-l an e

tre ated in one pass: for six- la ne or e ig h t- la ne

Model d evelopment

hi ghwa y ( t h ree - la ne two-wa y a nd four-lan e two-

Fi gure 1 illu tr at es a ge ne ra l prcading configura-

wa y. respecti vel y ). th e road

t io n a nd ass oc ia te d ge o me tric p ara me te rs for a

two p asses .

fo ur- la ne road ( two la ne ' pe r direc tion ).

(3 )

Ro ad wa y ty pe .

hall be t re at ed in

nowfall inte nsities a nd

ti me p eriod of a day can be cia ' ifi cd as needed

c...

l·

.J

or a p p roved by re pan ible agc ncie

( I. e . sta te

DOT ' ) . Fo r exa m p le . ro ad wa y ty pe m a y be cia -

Shou lder

ified into :! : u r ba n in ter ta te . II : ur ban arteria l. II I :

rur a l inters tate .

a nd

IV :

r ura l a r ter ia l :

now fall inte n ities ca n be classified in to : I : 0- 12.7

Und ivid ed Undivided

rnm/h , I I : 12.7-25 .4 mrrr /Ii , a n d 111: > 25 . 4 rnm /Ii , a nd tim e period ' of a da y ca n be clas ified int o: I : A M ( 6-9

I ) . I I : MD

II I: PM 0 -6 PM ) , a nd IV :

(l)

A M-] PM ) .

T ( 6 PM -(,

M ).

The determi nation of t r uck flee t .izc for prca d ing o pera t ion . con idcring geo m e t ry . we at her a nd tr a ffi c co nd iti o ns . is subjec ted to t wo es t iFig. 1 Geo me tr ical par am ete rs a mi spreadi ng

mat es . T he first e t imate e nsures t ha t th e tota l

patt ern of a road sectio n

a mo u nt mat e ri al s carr ied by th e t ru ck In Fig. 1: C it, i th e cen ter li ne mile of t he ma -

uff i-

cient to cover th e de ig nated to ta l lan e-m ile of

th e ce n ter line

.preadi ng , whil e t he seco nd o ne e n .ures th at th e

mil e o f th e acce le ra tio n/ decele ra t io n la ne . C R, i

tot al la ne - m ile ca n be t reat ed wi t h in th e pre- pee -

inline of th e road .cc tio n

~, i

th e ce n ter line mil e of ra m p . As s how n in Fig . 1 .

ified er ice t im e . A ' fo r m ula ted in Eg. (I ) . th e

fo r a four- lane hi ghwa y wi t h tw o lan es in each di -

two e tim at e

recti on. usuall y o ne sprea d ing t ru ck i

is c hose n as th e d ete rmin ed fl eet s ize . denot ed a

requ ired

w h ic hever yie ld ing a g re a te r va lue no w int en i ry

for pr eadin g t he t wo lane in one pass. Addition-

Y 1,ri,lV ' for truck type P > ec t ion s.

a l pre adin g patte rn ' will be suggeste d in th e fo l-

i . tim e per iod I . a nd wee kday o r wee ke nd

lowi ng pa rt in th i sec t io n .

v J

_ /"" U

-

•.

m ax

To co ns ide r th e ac tua l ro ad geo me t ry a nd .p rc ad ing pa tte rn applied to eac h road dur in g .p rcad ing opera t io n .

sum pt io n arc mad e in formu lating th e .a lt sp re a ( I ) Sp re ad ing rate ( q ua n t it y of chemica l

prca-

d in g pe r lan e mil e ) fo r a certai n road sectio n i w hic h

( A~

K 1') q

v si t ... I ,

(1 )

Nota t ions: • Sets P: { I . 2 . 3 } . a set of pread ing t ru c k t ype :

di ng p ro bl em:

co nsta nt .

{A.(L, + /R . ) . -A.-C: }

s E S . i E I ./ E T . w E W

ec tio n

th e fo llowi ng as-

IV .

m a y vary

in

d iffe re n t

no w

i. e . th ree ty pe ' of pread ing t ru ck

2 . 5-To n . 6-

To n . an d 1()-To n . S : { I . 2. ... . n }. a se t of road .ec tion .

=

events. Spread in g syste m ca n be ca libra ted to e n-

I : { I . 2 . 3 } . a .et of now int ensit ies: i . e. i

ure th a t proper a moun t of mat eri a ls i be ing a p-

I fo r 0- 12 . 7 mm / fu i = :2 for 12 . 7-25.4 mrri /h .

pli ed with varyi ng

preadin g truck

peeds on th e

a nd i

=3

for > 25 . 4 mm/h .

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5

Journal of Traffic and Transportation Engineering( English Edition)

T: {1, 2, 3, 4} , a set of time periods; i. e. t = 1 for AM (6-9 AM); t = 2 for mid-day (MD) (9 AM-3 PM); t = 3 for PM (3-6 PM); t = 4 for night time (NT) (6 PM-6 AM). W: {1, 2}, a set of weekday and weekend; 1. e. W = 1 for weekday and w = 2 for weekend. • Parameters C;: length of road section s , which can be determined by road geometry and spreading pattern. K p : capacity of the spreading truck type p, e. g. the carrying capacities for 2. 5-Ton, 6- Ton, and 10-Ton trucks are 4.25, 7 and 12 t , respectively. L s: total lane miles on mainline of road section s. q , spreading rate, e. g. usually, the spreading rate is 99 kg/km. This value may vary with the weather condition. R s: total ramp lane-mile of road section s. t s : required service time for spreading operation. v sitw: truck speed for road section s , under snow intensity i , during time period t , on weekday or weekend (w). Y psuw v number of trucks required for spreading road section s (including the mainline and ramps), under snow intensity i, during time period t , on weekday or weekend (w). Aa : adjusting factors account for the age of fleet. (i , e. Aa = 1.25 represents that 25% of existing trucks are under maintenance or have other obligations) . Ak: adjusting factors account for the capacity of the spreading truck. (i , e. Ak = 0.9 represents that the amoun t of salt carried by a truck is 90 % of the loading capacity in average) . Then, required number of trucks of type p for a maintenance yard which has more than one road section can be expressed as: n

r, =

(2::Yj>
r

sES,iEI,tET.wEW

as " * ". The rounding criteria are discussed next. Two criteria are introduced to round the estimated number of spreading trucks by acceptable spreading quantity adjustment and by acceptable service time delay. The purpose to set up acceptable spreading quantity adjustment is to compare the actual quantity of salt carried by the rounddown number of spreading trucks against the actual requirement. If the difference is less than the acceptable spreading quantity adjustment, denoted as /::"q., the round-down number is accepted, otherwise, round-up number will be used. As for the acceptable service time delay, denoted as /::,. t «» it is designed for comparing the estimated operation time with the round-down number of spreading trucks with the service time. If the difference is less than the acceptable service time delay, the round-down number of trucks is accepted, otherwise, round-up one will be employed. Note that the round-up is denoted by " + " and round-down is denoted by "- ". The two criteria can be expressed mathematically as follows. 3.1

Acceptable spreading quantity adjustment

The quantity difference (denoted as /::,.q) between the materials carried by the number of trucks and the actually required materials is expressed as n

n

llq(X)lx=Yp,i,w =Aa~(L,+R,)q-AkKp~Y;"itw (3) s= I

s> 1

where Y;sitw denotes the round-down number of spreading trucks. If the calculated quantity difference by Eq. (3) is less than the acceptable spreading quantity adjustment, then Y;'itw will be accepted; otherwise, the round-up ones denoted as Y;sitw will be used. The total number of spreading trucks (type p) may be estimated based on the criterion illustrated in Eq. (4) as:

(2:: Y { (2:: Ypsitw)

psuw ) -

Tp =

if Sq (x) I x = Y;"tw

~ Sq a'S

E S (4)

+

otherwise

(2)

In Eq. (2), T'; is the total number of spreading trucks of type p and n is the number of responsible road sections. However, as the calculation in the parentheses is not an integer, rounding up or rounding down should be considered and denoted

3.2 Acceptable service time delay

The time difference between the estimated spreading time and the service time, denoted as /::,. t , is expressed as a function of the round-down number of trucks denoted as Y;sitw' Thus,

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6

Steven I-Jy Chien et al. n

t. t ( x ) I x = y-psnw .

=

Aa I;

c:

. ~VsitwY;;tw 5=1

(5)

s=1

If t. t is less than the acceptable service time de-

lay denoted as t. t a' then

Y;sirw

will be accepted;

otherwise, Y ~rw will be suggested. The total number of spreading trucks (type p) may be estimated based on the criterion illustrated in Eq. (6) as: (6)

4

Data sources and data processing

The data required for the proposed spreading model include geometric, traffic speed and weather data, which can be retrieved from the straight line diagram (SLD), INRIX, and the Clams, respectively. A brief description of each data source and the method of mapping these data into an applicable format are discussed next. The SLD is a two-dimensional graphic representation of geometric characteristics of all types of roadways, including the interstate, U. S. and state routes systems used in several state DOTs such as New Jersey, Colorado, Ohio, and North Carolina. All the Interstate and State route information are included in SLD. After mapping each road section to SLD database, the information including lane number, lane mile and centerline mile of the mainline and ramps in each road section can be directly extracted from SLD database. However, as the lane number of a road section may not be constant, there will be more than one number extracted for a given road section and the spreading length of the road section can be calculated for each lane number. The calculation of the spreading length contains two parts: one is for the mainline while the other is for the ramps. For the mainline of two-lane and four-lane highways (with one lane and two lanes per direction, respectively), as the road can be spread in one pass, the total spreading length is equal to twice of the centerline mile of the pavement. For the

mainline of six-lane or eight-lane highways (with three lanes and four lanes per direction, respectively), as the road should be spread in two passes, the total spreading length is equal to four times of the centerline mile of the pavement. For the road sections with varying number of lanes instead of constant number of lanes, the spreading length can be calculated by combining the two different situations. For the ramps of a road section, as most ramps have less than two lanes, the spreading operation can be completed in one pass. Hence, the spreading length of ramp is equal to the centerline mile of the ramp. To take into account the reduced traffic speed on ramps, the spreading length of ramp is suggested as multiplying the centerline mile of the ramp by an adjusting factor. The weather and traffic speed data are archived based on geocodes of weather stations and TMC locations. The weather data, mainly obtained from the Clams, which provides an archive weather data collected by road weather information system (RWIS), include pavement temperature and status 0. e. wet, dry, and snow), subsurface pavement temperature, wind speed and direction, precipitation ( i. e. amount, occurrence, and type), water level conditions, humidity, and visibility 0. e. snowfall rate) at a 20 minute frequency. The temporal and spatial traffic data in this study are extracted from INRIX of which the data are anonymously collected from GPS-enabled vehicles and mobile devices through traffic message channel (TMC) and compiled into 5-minute-averaged speeds. The time varying weather information of those TMCs nearby the weather stations can be identified via a data mapping process, through which the speed matrix can be developed by correlating the speed data with roadway type, snow intensity, and time periods of a day as shown in Fig.2. When applying the speed matrix to Eq. (1) in calculating the number of spreading trucks for each road section, there are situations that some road sections may contain more than one roadway types. In such cases, a weighted traffic speed can be calculated and used as the traffic speed for that road section.

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7

Journal 01 Traffic and Tra nspor tation Engllleering( English Edit ion)

T ab.2 .

that t he w at her da ta a rc based on

01

2 1 :no v da y

du r in g 211 111 _11 11 • no w ' a on In

' e w Jer cy an d o nl) the dat a of \\ -ck duy

peed ma trr: fo r -ee kda

a rc e m-

I loycd in devel op in g the .pccd mal ri x \\ hich i to be use d in th e case s t udy. To e ns ure suff ici m t

fleet size d ue

10

traffi c co ngcs i io u in peak l ime

pe rio d s, the S,h pe rcen til e ' pee l! is e m p loyed as s peed . a I wh ic h 5'l,:, of I h e Ir a f'Iic is

I h e reference

rr a ve llin g be low Ih al .p e cd . If t he sp re a d ing truck

sp ed i high r than t hc , 'b pcrccru ilc 'peed . th e operation may Fig . ~

5

1 '\ '1 pm cnt oi tra ff ic vpeed ma tri

asc

c ued a: the I reading t ruc k

speed in the proposed model. An e xample of obtaining - I per cnt ilc peed I. illusrra t d in

Case study

In th e

c irn] cded by th e tra ff'i . and the

referen c . peed will

tu d y , th e a bove develo ped

F ig . .~ .

p read in g

m o del i- ap p lied to two highway m a int e na nc e ya rds in

I

~ oooo

'c v J c r cy . o ne in a n u r ban a rea ( ca lle d

w ith J ro a d sec t io ns ) a nd t h . o t he r on e i n

Y a rd

Highway c1n,>Ificnlio n I peed distr ihu tion '" TP-AI-I &. SI

a ru ra l a rea (ca lle d Ya rd B wi t h fou r ro ad sec -

s· per cent ile

tio ns i , Th e road ge o me t ry da ta and Iraffie d at a

pee d :1 mph

under va r ious w 'a t he r co n d it io n in different lime period ' of a day for ca . h . ectio n a rc summarized in Tab , 1 and E,

I'h

Ilcct

izes needed for the

"tud . yard ' und ' r d iff rent ci r umsian c ar then analyzed . a

'o tc that Sc l io n A- I in Ta b . 1 onsists

segme n ts w it h di ffere n t ro ad type

II ( urba n

1·'ig . 3

Illu strat ion 01 ",. 1'<:c001 tr iburion cur' c

a rte rial> , III ( ru ra l int er sta te ) , a nd I V ( ru ra l arA s ca n be observed i n Tab. 2 so m e speed d a t a .

tcria l ) . a n d all sec t io n: d esi gnat ed 10 ya rd B belon g to road t pc I ( u rba n inrcr suu . >.

m a r ke d a s " - ". arc una b le to be ge ne ra te d d ue to i nsu ffi ci e n t

B. m a pp i ng th e roa d geo rnc t r s : t ra f f ic .pccd .

'I readi ng t ru k

t h o sc

.p .c d is te nt a tive ly

tn e . ' no w intcn sity . and lime period of a day

assumed nOI affe red b y th e traffic SI ec d and th e

during \ eckda y

re ro m mc nd cd operation '1 .c d i

. m p lo yed a - a

R

' 0. '\ ' \

1\

II

.

m,

pc

III

~

12. 7

"'·1. 2

1\ ' ,\

III

11, .1

')7, ..2

J

IJ ••

I I. ;;

~

(j..

h , II

.«

54, -

(. ,11

4 .1 1

74. 5

~

\

~

I

'I

~

1.

III

H·~

-

IV

J\· 1

U· I

7

.h .

. ,

20]4 China ",QllQel1[1J'c Journal Electronic Publishing House.

i

'I

3; . .3 ;

II II

P.3

?]

Pa r

and wea ther da ta . t h c ' peed m at rix by roadway arc obtained and pre: .n te d in

. th e

tra f' Iic a nd , or wea th er dur a .

II I

I I

righ

ed,

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,-

3-. ~

.net

8

Steven I-Jy Chien et al.

Tab. 2 Traffic speed matrix (weekdays) MD

AM

HC

II

III

IV

Snow intensity

PM

NT

Mean

5th 010

Mean

5th %

Mean

5th %

Mean

5 th %

(km/h)

(km/h)

(km/h)

(km/h)

(km/h)

(km/h)

(krn/h)

(km/h)

87

45

93

71

93

64

95

74

II

82

39

84

32

89

52

III

87

27

95

40

90

53

76

42

76

40

79

50

II

72

40

82

61

76

48

III

74

35

68

27

74

48

97

69

101

84

100

84

II

92

71

97

76

89

55

III

82

37

95

71

89

58

90

68

90

69

92

71

87

69

89

76

90

71

92

82

90

68

II

III

74

101

90

35

85

69

Note: lkm/h =0.62 mph; HC-highway classification; .. - "-not available.

substitute. The required fleet sizes under different circumstances for both yards are estimated. The calculation details for Yard A under snow intensity III during the AM peak (6-9 AM) is illustrated and discussed next. The spreading truck speed for each road section can be determined by comparing the recommended spreading truck speed 0. e. 48. 3 km/h (30 mph» with the reference speed. For both Sections A-2 and A-3 of Yard A, the reference speed of 37 km/h (23 mph) is used as the spreading truck speed, because it is less than the 48.3 km/h (30 mph). Similarly, for Section A-l (containing three types of roadways) the spreading truck speed is 41. 1 km/h (25.6 mph) which is calculated based on the weighted average (35 x 37% + 37 x 21% + 48. 3 x 42% =41. 1 km/h). The developed model is applied to the seven road sections of two yards with a predetermined service time limit of 1. 5 h considering (1) single type of spreading trucks and (2) multiple types of spreading trucks. Constant spreading rate of 99 kg/km is assumed, and the acceptable spreading quantity adjustment and acceptable service time delay are set as 45 kg and 15 min, respectively.

5.1

Operation with single type of spreading trucks

In this case, single 6-Ton spreading trucks are used for the spreading operation which can carry 7 t of material. As each road section may have different spreading patterns due to varied road geometry and roadway types, the required number of trucks for each road section is calculated separately. The result for the yard based fleet size can be obtained by summing up the results for each road section according to Eq. (2). In order to calculate the required number of spreading trucks for each road section, Eq. (1) can be applied. It is found that 1. 59, 1. 85 and 2. 19 of 6-Ton trucks are required for each of the three sections of Yard A. Hence, the total required fleet size for spreading is 5. 63. In the calculation of the required number of spreading trucks, it is observed that the estimate of the total salt quantities in Eq. (1) is much stricter than that of the service time. As a result, when rounding the fleet size to an integer, the criteria by acceptable spreading quantity adjustment shall be applied. According to Eq. (3), it can be obtained that by using the round-down number of trucks (5 trucks) it introduces the

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Journal of Traffic and Transportation Engineering(English Edition)

quantity difference of round 3629 kg between the total quantity of salt carried by the round-down number of spreading trucks and the actually required quantity of salt. This is far beyond the acceptable the spreading quantity adjustment of 45 kg; as a result, the rounding up result is emplayed, and six 6-Ton spreading trucks aye suggested for the Yard A. The number of spreading trucks required for both yards under all different circumstances are obtained similarly and presented in Tab. 3. Tab. 3 Yard

Estimated fleet sizes with 6-Ton trucks Time period

Snow intensity

AM

MD

PM

NT

6

6

6

6

II

6

6

6

6

III

6

6

6

6

5

5

5

5

II

5

5

5

5

III

5

5

5

5

ry greatly during the time periods of AM peak and MD period mainly due to the low traffic speed (see Tab. 2). By comparing Tables 3 and 4, it can be concluded that for low capacity trucks, the required number of spreading trucks is mainly determined by the total required quantity of the spreading materials for the yard, while for the high capacity trucks, it is mainly controlled by the traffic condition and service time limit. As a result, to make high efficient use of the winter maintenance resources, it is preliminarily recommended that for the road sections with low traffic speed, the low capacity trucks are preferred, while for the road sections with high traffic speed the large capacity trucks are recommended. 5.2

A

B

It can be observed that the fleet size for both

Yards A and B do not vary for all snow intensities during different time periods, which denotes the required quantity of 6- Ton spreading trucks is not dictated by the traffic condition and service time limit, but determined by the constrain of total required materials. It is expected that this situation will be different for high capacity trucks. To confirm this, the simulation with lO-Ton trucks is conducted with results presented in Tab. 4. Tab. 4 Yard

A

B

Estimated fleet sizes with 10- Ton trucks Time period

Snow intensity

AM

MD

PM

NT

4

4

4

4

II

4

4

4

4

III

5

4

4

4

3

3

3

3

II

4

5

3

3

III

5

5

3

3

As can be observed from Tab. 4, the results va-

Operating with multiple types of spreading trucks

In case two types of trucks are employed for spreading operations: 6- Ton trucks with carrying capacity of 7 t and 10- Ton trucks with capacity of 12 t. The model developed in this study can also apply to estimate additional trucks by type considering the quantities of existing truck types already in place. For example, assuming that only two 6Ton trucks are in place for a designated network, the needed number of 10- Ton trucks can be determined by Eqs. (1) and (2). First, the total quantities of salt carried by the two 6- Ton trucks and the spreading length can be calculated. Considering the capacity adjusting factor of 0.9 and spreading rate of 99 kg/km, total quantities of salt carried by the two 6- Ton trucks is 11430 kg, which is equivalent to 72 lanemile spread. If the spreading trucks speed is 48.3 krri/h , the total spreading length of the two trucks during the service time of 90 min is 145 km. To estimate the required quantity of trucks for Yard B under snow intensity III during the AM peak (6-9 AM), subtracting the lane mile to spread and the spreading length by the two 6-Ton trucks from Eq. (1), there is a need for additional 3.05 trucks (10- Ton) to complete the work. According to rounding criteria presented Eq. (6), the number of 10- Ton trucks is rounded to 3. Sim-

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10

Sleven I-Jy Chien et 81.

ilarly , the

I'

pre erued in

ull

for all oth

I'

um tanc

II'

ar

M and

10 tim

ing single t

ab.:-.

. of preading tru k 6- Ton and 10-

Ton . re p cti el . The

I'

ll ' •

2

2

II

2

III

2 2

8

• ' o te ,

~ . ~

MD

M

Intensit y

II

2

III

2

2

2

"2

II

2

2

large truck

I'M

"

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

- type I truc k ( b- To n) ;

~

.•

2 ~

-

are pre

ru d in

indicat ed in Fi g . 4 and 5 , the fl eet ize with

Timc period Yard

ult

I'

Fig . -t a nd 5 . rc pcct ive l s :

t ius .. ith multiple truck t) pes

Snow

con id ring by emplo-

period

2

2

2

2

2

2

( i. e . IO-Ton ) increase a

th e

now

in te n it y increa cs in th e A I pe a k a nd MO pe ri o d. A

the serv ice ti me co ns trai n t is th e pri mal'

fac tor affec ting t he requi red fleet .ize under thi

situation , it i se n sitive to the w ath er condition ' ( i , e.

now inten sity )'. H o we er . for ' m a ll truck

see m s not affected b.

( I . e . 6-Ton ) . the fleet iz

the now int cn ity and time o f a d ay for the rud y yard . whi h i ' mainly dict ated by the total

type II truckt Ill- Ton I.

a mount of spreading ma terial '. Thu . the impa t of red uced traffic

By compar in g the re ult s of th e ca e with in glc type o f IO-To n sp re ad ing t ruc k ' C r a b . ·1) wi th th at

peed due to adverse weather

seem in signif ica nt. I n addit ion . as e x pec ted , the 'e n .itivity of th e fl ee t izc to th e wea ther cOI1lJi-

of the ca 'e w it h t he bo t h typ es of t ru c k ' . it c a n be

l ion i hi gh e r in u r ban a rea th an th at in rural a re a

found t hat us ing mixed I pe of s p rea d ing truck '

m a inl y d ue to th e lowe r t ra f f ic speed in u rban ar-

lead to ad' rca .c of t he fleet size . which can be

ea ( ee Tab. 2 L

considered to opti mize the u tiliza tion of \ inter maintenance rc 'o u r e

durin g

'I reading opera-

tion.

5.3

preadin g ra te i al which is d efined a pread per Ian

Sensitivity analysis

0

the a mou n t o f materi al

to

mile . It ma y vary depending on

geo me t ry and \ cat her condition.. To invc ui gatc

cco rding to analysis re ults pre cntcd in Tab '. a nd 4 . th e var ia t io n of fl e et size m a inl y o ccu r ' du r in g A I a nd

a critical actor to deter-

0

mine n eed ed fl · 't size for .p r .ad ing operat ion .

10 tim e pe ri od ' . II is noted he n :

t hat a ' th e ' pee d da ta a rc not co m p le te fo r th e PM peak . hence . th e varia t io n o f fl eet size durin g

it effect . the required fleet .ize under thr e different

pre ad in g ra te ' ( i. c . 7 1.

dur in g the

1) 1)

,

127

kg / k m )

M peak a rc a na l ze d . T he result s are

pre e n te d ill Fi g , (I, A ind icat ed in F ig . 6 . th e fi e °t izc . in ge ner-

PM pe ak i no t repro e n ra tivc. To in vc ti gar e th e

a l . increase

effec t of now in tcn ity o n fleet ize . a en irivi ry

both typ e of tru k ' and this trend is more obviou

analy i i

for the yard in rural area than th at in the ur ban

...

~

performed for both yard

pre a d ing ra te increases for

6r

r

;: SD--

-

-

-

-

-

-

-{J--

-

-

-

-

-

--::::::C

~ ;:;

u...

-0- 6, Ton trucks

." ... S

-6- 10- Ton tr uck

0:::

during the

as jh e

.. ..

U 0:::

"" 4 ;:;

;:;

,§

E

.,

Ul 4l r -- - - -- -
t.:J

3

2 IL.

-:

~

2

3

2

now intensi ty leve l (a) Yard A in rura l area

3

now intensi ty level (b) Yard B in urb n area

Fig . 4

Fl e t iz vs.

11994-2 14 China Academic Journal Electronic Publishing Ho

no w in tensity (

. All righ

M pc . I

reserved.

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.cnki.net

II

Journal 01 Trallie and Transportation Engineer ing ! English Edit ion)

6

,~

b~G--------"D---------{j

;;

"

.~

;:;

-D- o-Tou u uck

"

<::

r:: "

-6- 10 -Ton truck.

.."

;";

-D- o-To n tru cks

~

-6- 10·Ton tru cks

.§ r.

~ lr----------t.~--------6

~

J'-------.1-2

I

2 nowmien ity level (bl Y rd B in urban area

3

now inten ily level (a) Yard In rural ares

Fig. S

Hee l size

"S.

3

snow in rc nsi t ' ( M D period )

q

.

-D- b-Ton truck

-D- 6-Ton tru ks

-6- 10-Ton tru ek

-6- to·T onlru

.~ 6

::::

~

c;

;:;

" -e ;";

<::

"

<::

.." 5 ~

E 5

.§"

~

~

99 ' pre din' r le(kglkm ) (a, Vard'\ In rural area

.1.P'foc=--- - - - -- '''-- - - - -- - -A

99

1.' -1

12

preudin ralc(kglkm ) (b ) Yard B in urban area F1 ct oil

I'lg . i .

v v;

prcading r••rc

ther in an urban area .

arca . The main factor con tributing to this region-

one in a rural area and t he

al effec t i. th e lo w tra Iic ' pee d in u r ban area

W it h t he collec ted \ ca ther . geometr . and traffic

w h ich red uces th e effec t of sp re adin g ra te o n flee t

d ata . as p .c d matrix sub jec t to va r io us d imension s

size . Mo reove r . th e sp rcadi n g ru tc ha s more .ig-

( i. e. road v ay typ e. ' no w inte nsi ty . a nd tim e of a

nificant inf luen ce on the ' ma ll ca pac ity t ruc k '

day ) is d .vc lo ped , It is found t h a i t h e model is

t ha n tha t on the la rge .a pu it)' one due to limi ted

fai rly practical and cf'Icc t ivc

tru k apa it )' .

6

ational ond ition: .

Conc lu si o n s

In th is

tudy . a mode l

tu est imate f lcct .ize . e sp . 'ia ll y in raptu ring th e diver ' it) of o p r -

A scnsi t iv it d e veloped to c t irnat

th

re la ion hi p

a naly

co nducted to e xplore

ctw e c n m ode l p a ramete r- a nd ~

flee t size ' o r spread ing 01 cru tion ' o n idcri ng roa d

f' lcet size, A ind i at J In Fi g - . . and

ge o m e t ry . we ather and tra ffic . w hi ch is ca pab le

s ize wi th large truc k '
of c a ptu r ing the hc icro ' cn e ity of

the

S

.r vicc la ne -

mile . spreadin g rate ' and pa ttern ' . traffi and Huck

I)

I c . \\ hile est imating fleet

rnethodologi ' a l a pproa h o f pro c

' peed : ize . .

in g and ma p-

ping g ornetry . \\ a th r , a nd tra f i data fo r g -n cratin g th e peed rna t ri: i di:c u cd . In ca c

ud-

y . t he proposed m o d el is a p p lie d to e .rima rc flee t size for two maint en an ce

1994-2014

-a rd

in

I

le w J c r

cy .

the f lc ct

now in ten sity in crea se s in the I\ M peak a n d

MD period . because the service time constraint is the I rirnary fa tor a ffe ctin g the req ui re d fl ee t .ize . t h u . it i . en it ivc to th e wca her o ndi tio n i. e .

now irucn ity }. H o w e ve r . fo r mall tru

( i. e . (,-To n ) . th

fie t izc : -e rns no t alit: te d

~

th e ' no w intc n siry a nd rime of a day for t he s tudy a rd . whi ch is mainl y dicta ted

ina Academic Journal Electronic Publishing House.

rights reserved.

b.

the total

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12 amount of spreading materials. Thus, the impact of reduced traffic speed due to adverse weather seems insignificant. In addition , the fleet size increases along with the increase of spreading rate and the influence is more significant on the small capacity trucks than that on the large capacity ones. The results also show the regional effect of traffic speed on spreading operation that the impact of snow intensity , traffic speed and spreading rate on fleet size could be greater for the yard in an urban area than that in a rural area . This research lays the basis for the application to deploy resources during winter highway maintenance , such as assisting transportation agencies to allocate numbers of trucks over different yards. The developed model can also be applied to evaluate operational performance under various scenarios, such as partitioning a regional network into small sectors subjected to workload and contiguity constraints as discussed in a study conducted by Perrier et al. ( 2006 ; 2010 ) and winter highway maintenance resource optimization .

Steven I-Jy Chien et al. and spatial variations of highway traffic volumes. Journal of Transport Geography, 16(5) : 358-372. Daniel, J. , Chien, S. I. , 2009. Impact of adverse weather on freeway speeds and flows. TRB Annual Meeting, 09-2837. Federal Highway Administration, 1995. Manual of practice for an effective anti-icing program: a guide for highway winter maintenance personnel. Report No. FHWA-RD-95-202. Federal Highway Administration , 2003. Intelligent transportation systems and winter operations in Japan. Report No. FHWA-PL-03016. Federal Highway Administration, 2006. Empirical studies on traffic flow in inclement weather. Report No. FHWA-HOP-07-073. Federal Highway Administration , 2009.

Weather-responsive traffic

management: real solutions for serious traffic problems. Report No. FHWA-JOP-09-035. Federal Highway Administration , 2010. Traffic analysis toolbox volume XI: weather and traffic analysis, modeling and simulation. Report No. FHWA-JP0-11-019. Federal Highway Administration , 2010. Data mining and gap analysis for weather responsive traffic management studies. Report No. FHWA-JP0-11-037. Federal Highway Administration , 2012. Guidelines for the use of variable speed limit systems in wet weather. Report No. FHWA-SA12-022. Hanbali , R. M. , 1994. Economic impact of winter road maintenance on road users'. Transportation Research Record, 1442 : 151-161. Liang, W. L. , Kyte, M. , Kitchener, F. , et al. , 1998. Effect of

Acknowledgments

environmental factors on driver speed: a case study. Transportation Research Record, 1635: 155-161 .

This work is supported by the New Jersey Department of Transportation and the Federal Highway Administration . This support is gratefully acknowledged.

Massachusetts Highway Department, 2006. Snow & ice control gener-

References

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Agarwal , M. , Maze, T. H. , Souleyrette, R . , 2005. Impact of

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Andrey, J. , 2010. Long-term trends in weather-related crash risks. Journal of Transport Geography , 18: 247-258. Chien , S. I. , Schonfeld , P. , 20Cll . Optimal work zone lengths for four-lane highways. Journal of Transportation Engineering, 127 (2) : 124-131 .

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Research, 33: 209-238. Perrier, N. , Campbell , J . F. , Gendreau , M. , et al. , 2010. Vehicle routing models and algorithms for winter road spreading operations. CIRRELT-201 0-53. Perrier, N. , Langevin , A. , Campbell , J. F. , 2007. A survey of

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models and algorithms for winter road maintenance. Part Ill: Ve-

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hicle routing and depot location for spreading. Computers & Op-

Transportation Engineering, 128(2) : 145-155. Cifelli , N. J. , Cunningham, W. B. , Dunn Jr, J. F. , 1979. New Jersey department of transportation model for winter equipment and manpower allocations. Transportation Research Board Special Report, 185 : 82-84. Dacia, S. , Sharma , S. , 2008. Impact of cold and snow on temporal

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