The effect of intersector dispatching on police patrol performance

OMEGA Int. J. of Mgmt Sci., Vol. 15, No. 5, pp. 411~,17, 1987 0305-0a83/87 $3.00+0.00 Printed in Great Britain. All fights reserved Copyright ~ 1987 Pergamon Journals Ltd

The Effect of Intersector Dispatching On Police Patrol Performance

GARY M KERN

University of Notre Dame, Indiana, USA

(Received September 1986; in revised form January 1987)

The experiment reported here concerned the relative effect of intersector dispatching on police patrol performance. Using a computer simulation model, it was found that the inclusion of intersector dispatching can have a significant impact on patrol response time. This should he of interest to patrol administrators and researchers who study this area. Despite the anticipated problems in its implementation, intersector dispatching holds great promise for improving patrol operations.

INTRODUCTION

POLICE PATROL operations provide MS/OR researchers with a rich set of deployment problems. Police are expected to respond to citizens' calls for service (CFS) whose urgency varies considerably. As opposed to fire and ambulance service, police are also expected to patrol geographic areas.

Previous researchers (e.g. [2], [3], [4], [11]) have suggested numerous management science models whose use would improve patrol effectiveness by improving patrol deployment. These models focus on the design of geogaphically-defined patrol regions called commands (that are divided in sectors, or beats), the assignment of available patrol units to sectors (geographic allocation), and the assignment of available patrol units to CFS (dispatching). The models are expected to improve the performance of the patrol force without requiring additional patrol resources.

One tactic suggested by researchers ([10], for example) is intersector dispatching. Intersector dispatching increases the number of units eligible to serve a CFS by looking beyond the boundaries of the sector when a CFS arrives. If the unit/s in the sector is/are currently not available, a unit from outside the sector may be assigned to serve a newly-arrived call. Inter- sector assignment can, in effect, cause the dynamic reallocation of the patrol units geo- graphically.

This paper examines the ability of intersector dispatching to improve patrol performance. The paper will answer the following questions:

1. Does using intersector dispatching improve patrol performance? Although some testing of intersector dispatching has been performed [9], further investigation is needed.

2. How does the magnitude of improvement compare with that provided by improving the geographic allocation of units?

The improvement caused by implementing intersector dispatching can be related to improvements caused by other changes in deployment. One such deployment change of interest is geographic allocation.

Patrol administrators will find the answers to these questions of great interest. They often hesitate to implement intersector dispatching for several reasons (see [1], [15]). Patrol officers may not perform service at the same level of effectiveness in a 'foreign' sect'or. Lines of direct command may become confused. Most significantly, intersector dispatching is a soph- isticated dispatching tactic which places added demands upon communications personnel and resources. Operators and dispatchers, who typically focus their attention on specific geographic sectors, must be provided with timely and clear information concerning the status of all patrol units located across the entire command. Com- munications resources (e.g. radio channel fre-

411

412 Kern--The Effect of In tersector Dispatching on Police Patrol Performance

quencies, broadcasting equipment) must enable any dispatcher to contact any patrol unit.

However, if intersector dispatching con- tributes significantly to the improvement of performance, means of making its implementation possible may be warranted. Patrol administrators and researchers may find justification for addressing the logistical and technological problems involved in the implementation of intersector dispatching.

PREVIOUS RESEARCH

Several researchers have focused their attention on developing models to improve the allocation of available patrol units to commands and sectors [2], [3], [4], [6], [7], [10], [13], [16]. These models typically considered the form of dispatching as a factor in the formulation of the allocation. Dispatching has often been viewed as an input in the formulation of an optimal geographic allocation of patrol units.

Larson presented the concept of intersector dispatching and illustrated that

" ' . . . i t is not unusual on a given tour for a patrol unit to respond to more calls outside its own sector than inside" [I0], p. 242.

He used simulation as well as analytical for- mulations to describe these properties. His work concluded that further study of intersector dispatching was warranted.

Kolesar and Walker also included intersector dispatching as a factor in their simulation model [9]. The authors did not present results de- scribing the relative merit of implementing intersector dispatching.

METHOD

The research questions posed in the introduction require the systematic comparison of patrol deployments that include the use of intersector dispatching and those that do not. A computer simulation model was designed and used to assess the relative performance of several deployments in a single hypothetical city that is described below.

This study focuses on the behavior of a single command. The command is assumed to be square in shape and is divided into quadrants that form the sectors. It should be recognized that this is a rather simple environment; al-

though it allows for generous intersector activity (when available), the results of the experiment should be considered within the context of these environmental limitations will be addressed later in this paper.

The physical size of the sectors affects the average travel times of patrol units on intra- sector and intersector trips. Figure 1 depicts the sector design. All travel times are assumed to be exponentially distributed. It was assumed that it took an average of 0.5 minutes for a patrol unit to travel from any location within its assigned sector to another within the same sector. This value reflected the knowledge of the sector's geography that an officer is expected to have. Intersector travel times were adjusted to con- sider the longer travel times caused by the officer's lack of intimate geographic knowledge of the sector. Intersector travel was measured as Euclidean distance. This is a simplifying assumption that should be addressed in further research.

Twenty patrol units were available for deployment. (Other patrol force sizes were studied for the relative effect of this factor. Patrol force size was not found to have an influence on the relative effect nor magnitude of these effects. Details are available from the author.) A patrol unit is composed of one patrol car and one patrol officer. It should be noted that some cities include two officers per unit, while other cities use one per unit (see [7], for example). The selection of one-officer units requires the assignment of two available patrol units to serve an urgent or high-priority call. It is assumed that service of urgent calls by only one unit would place the officer in a position of unnecessary danger.

Sector one ( 4 0 % of CFS) Sector Two [ 2 0 % of CFS)

Sector three (20% of CFS) Sector four ( 2 0 % of CFS]

Average distances (measured in trave I. minutes )

TO s e c t o r

One Two Three Four One O.S 4.0 4 .0 5.7

From Two 4.0 0.5 S. 7 4 .0 sector Three 4.0 ,5.7 0.5 4 .0

Four ,5.7 4 .0 4.0 O.S

Fig. 1. Geographic layout.

Omega, Vol. 15, No. 5 413

Demand is considered to be a set of CFS arriving in a random manner at the police department 's dispatching center. The calls are divided into two levels of priority. Priority level one calls are assumed to be urgent and priority level two calls are of a less urgent nature. Based upon previous findings [17], it was assumed that 20% of the CFS were priority one calls and that 80% were priority level two calls.

CFS also vary by location of the incident. It was assumed that the frequency of occurrence in sector one was twice as high as any other sector. As the CFS arrive, 40% are located in sector one and 2 0 0 are located in each of sectors two, three, and four.

Patrol service times of CFS have been found to be exponentially distributed (see [6], [7]). It is assumed that it takes two patrol units an average of 60 minutes to serve a priority one call in the experiment. It takes an average of 40 minutes for one unit to serve a priority two call.

The final parameter needed to define demand is the interarrival times for CFS. CFS interarrival times have been found to follow an exponential distribution [t2]. It was decided to analyze the behavior of this system under both relatively low demand rates and relatively high demand rates to see the magnitude of performance improvement that intersector dispatching could contribute. A range of average interarrival times was studied. Previous research suggested a relevant range of interarrival aver- ages.

The degree of demand pressure being placed on the patrol system can be expressed in terms of R ' ,

R' = Sum(/= 1 . . . . . N): [(l,)(f)(ah/(m,)(P)].

where

l~ = interarrival rate for CFS type i f = relative frequency of occurrence of CFS

i ai = number of units dispatched to CFS i

mi = service rate for CFS i N = number of CFS types P = total number of patrol units available.

The R ' values used for this experiment were 0.311, 0.4, 0.467, 0.56, and 0.7. These values were based upon previous work by the author.

Various deployments were applied to the environment just described. The performance of the deployments were collected and then ana-

lyzed. The analysis and conclusions drawn from the results are discussed in a later section of this paper.

Changes in patrol deployment are expected to improve patrol performance. Although the ulti- mate goal of police patrol is to intercede in current CFS and prevent the occurrence of future CFS, these are difficult measures to quan- tify. Instead, researchers typically rely on measures of patrol efficiency. Response time has been used as a major patrol performance crite- rion in several previous studies [2, 11].

Workload equity is another performance measure of interest. Patrol officers are concerned about the relative amount of patrol time they log in relation to the other officers on duty [1]. Patrol time range was measured in this experiment. Patrol time range (p) can be expressed as

p = max(/= 1,2 . . . . . s) {u,} - min(i = 1.2 . . . . . S){u,}

where

u~= average relative time patrolling for all units in sector i

S = total number of sectors.

The optimal value for patrol time range is zero, the worst case would be a value of one.

These performance measures were collected during simulated operation of the deployments in the hypothetical command.

DEPLOYMENTS

Deployments are varied in terms of initial patrol unit geographical allocation and dispatching rule. Three allocation heuristics are used to assign patrol units to sectors. The units are assigned (1) equally to each sector, (2) by relative CFS arrival rates within sectors, or (3) in an intermediate manner. The various allocations of the 20 patrol units are illustrated in Fig. 2. (The purpose of this experiment was not to perform a direct comparison of various geographical allocation techniques. No conclusions concerning relative allocation techniques are intended nor implied.) There are also three dispatching rules available: (1) no intersector dispatching allowed, (2) intersector dispatching is allowed for urgent CFS, or (3) intersector dispatching is allowed for all CFS.

The performances produced by the nine deployments were collected and analyzed. The

414 Kern--The Effect of Intersector Dispatching on Police Patrol Performance

ALLocation one: ~-quoLLy to each sector

5 5

5 5

ALLocation two; ReLative CFS arr iva l rotes

8 4

4 4

ALLocation three: An intermediate aLLocation

6 5

5 4

Fig. 2. Geographical allocations of 20 units.

following section discusses the analyses of these simulation results.

RESULTS AND ANALYSIS

A discrete-event computer simulation has been designed using SLAM [14] and making extensive use of FORTRAN subroutines. The simulation model is capable of following any of the three intersector dispatching rules listed in the previous section. A detailed discussion of the simulation model can be found in [8]. Points concerning the model's processing that may affect the results of this study include:

1. When a CFS arrives, the dispatcher at- tempts to assign units located in the same sector as the CFS. If no patrol units are available and intersector dispatching is not allowed for that type of call, the call is placed on a queue. If intersector assignment is allowed, the search for available units continues in adjacent sectors until a sufficient number of available patrol units is located. If insufficient units are available in the entire command, the call is queued.

. If intersector dispatching is allowed for a particular CFS, the search for available patrol units begins with the sector judged closest to the location of the CFS.

. Upon completion of service of a CFS, patrol units travel back to their patrol location. During this time, the units are assumed to be not eligible for subsequent call assignment. Although this sounds to be quite a strict assumption, it follows actual experience rather well [1].

. Service of any CFS does not begin until all assigned patrol units arrive at the CFS location. Typically, patrol officers are cau- tioned against responding to dangerous sit- uations without the presence of appropriate back-up.

The replication lengths for this experiment were calculated using Fishman's subrun method [5], and a transient state existed during which data was not collected for analysis. The simulation was started with a set of common random number seeds for each deployment's analysis. Therefore the comparison of the deployments is across exactly the same demand stream. Five replications were performed for each deployment and demand-environment combination. The output of the five replications were aver- aged to produce the results for the deployment. The results are grouped and analyzed to answer the research questions posed earlier.

The results are presented here using both graphs and summary statistics. The statistic employed is Friedman's two-way nonparametric ANOVA. Friedman's two-way nonparametric ANOVA (henceforth called "the Friedman test") does not require assumptions concerning the normality of the data to be analyzed. Because common random number seeds were used, and because only five replications were performed for each deployment-R' combination in the simulation, assumptions of normality are suspect. The Friedman test has been shown to be quite effective in previous applications [18].

The results and analysis will be discussed according to the research questions posed earlier. 1. Does using intersector dispatching improve patrol performance? The results shown in Fig. 3 (average response time to all CFS) are most graphic. Figure 3 shows the performance of the nine experimental deployments as divided into three clusters. The three clusters are formed by the varying degrees of intersector dispatching


2O t 9

18

17

"E 1.5

• - 12

11

,- 10 o

7 g 6 P 5

• 4

3

2

1

0

Friedman • 39.3, siq - 0 . 0 0 0

I I I I 0 . 3 0 .4 0 .5 0 .6 0 .7

R ~, d e m a n d r o t e

CJ = ALLocot ion one, no in te rsec to r o =AU~ocot ion three, no intersector A = A t L o c o t i o n two , no oU.ocot ion + • A L loco t ion on'e, i n te rsec to r for p r ioCty one ¢oU_s X =A( . I .ocot ion three, intersector fo r p r i o r i t y one

• A L L o c a t i o n two, Jntersector fo r p r i o r i t y one (~ . A U . o c n t i o n one, a l l i n t e r s e c t o r • • ALLoca t i on th ree , ol.I intersector

• ALLoca t i on two , a l l i n t e r s e c t o r

Fig . 3

allowed by the deployments. The worst- performing group (that with the highest average response times) all disallow intersector dispatching. The best-performing group (that with the lowest average response times) allowed intersector dispatching to all calls. The effect is most pronounced at the higher values of R'. The Friedman test supports the findings that there is a statistical difference in the performances rep- resented by the lines on this figure. The implementation of intersector dispatching certainly reduced average response time to CFS and thus improved the performance of the patrol force.

Figure 4 depicts the graphic results for patrol time range. Note that a pattern is different from that found in Fig. 3 above. The best patrol time range results for the nine deployments use the same allocation, regardless of intersector dispatching. This indicates that the improvement of geographic allocation may have a greater effect on workload equity measures.

The first research question can be answered affirmatively. Intersector dispatching can significantly improve certain factors of patrol

performance. The degree of improvement caused by implementing intersector dispatching will increase with the degree of demand (R') that the patrol force must serve.

2. How does the magnitude of improvement compare with that provided by improving the geographic allocation of units? This question asks for a relative comparison of the improvement caused by changing allocation and the improvement caused by introducing intersector dispatching. Figure 5 illustrates such a comparison for average response time. Each line on the figure shows the percentage improvement created by fixing one parameter (geographic allocation or intersector dispatching) and then allowing the other to vary. Please note that, as opposed to the two previous graphs, the higher the value on this graph, the more attractive the result is that it represents.

As can be seen in Fig. 5, improvements brought about by introducing intersector dispatching, regardless of the allocation in effect, can create significant improvements in average response time. Improvements created by changing allocation, although noteworthy, are only a fraction of the size of those resulting from allowing intersector dispatching. Again, the Fri- edman test supports the assertion that the performance data used to compose the different lines are from different populations.

Patrol time range is not affected in the same manner. As shown in Fig. 6, patrol time range

0.5

• 0 ,4

o L. 0.3

E • ~ 0.2

~- 0.1 o

0.0

F r i e d m a n - 31.0, s ig - 0 . 0 0 0

~ ~ t "~ 0 .3 0 .4 0 .5 0.6 0 .7

R: d e r n o n d r a t e

r l . A l l o c a t i o n onet no i n t e r sec to r -+-(3-I- . A L L o c a t i o n three, no i n t e r s e c t o r -t-+-I- . A L l o c a t i o n one, p r i o r i t y one intersector

• A l l o c a t i o n three, priority one i n te rsec to r ÷ - A L L o c o t i o n one, a l l i n te rsec to r o - A L L o c a t i o n three, a l l intersector v - A l l o c a t i o n two, a l l i n t e r sec to r X = A L L o c a t i o n two, priority one intersector A - A U . o c o t i o n two, no i n t e r s e c t o r

Fig . 4

416 Kern--The Effect of Intersector Dispatching on Police Patrol Performance

1.0

• 0.9 E m

0 . 8

C o 0 . 7

0 . 6

c

~ 0 . 5

o 0.4

E 0 . 3

g o.2

q~ u

~, o.~ Q.

0 . 0

Friedman l 2 2 . 8 , sig I 0 .001

X

I I I I I I 0 . 3 0 . 3 4 0 . 3 8 0 . 4 2 0 . 4 6 0 .5 0 . 5 4

R ~, d e m a n d r o t e

& =ALLoca t i on one, dispatch varying 9 • ALLocation three, dispatch varying X • ALLocation two, dispatch varying n • N o intersector, aLLocation varying + = P r i o r i t y one intersector, aLLocation varying • • ALL intersector, aLLocation varying

Fig. 5

A

g e- o

o

¢-

o

g

0

r_

Friedman = 21.2 , sig • 0 . 0 0 2 1 . 0 - -

0 . 9 - -

+ X------ .-__ x - - X

0 . 7 -

0 . 6

0 . 5

0 . 4

0 . 3 1

0 . 2

0 . 1

0 . 0 I I I I I I 0 .3 0 . 3 4 0 . 3 8 0 . 4 2 0 . 4 6 0 .5 0 . 5 4

R~ d e m a n d r a t e

rn . NO intersector, aLLocation varying x • ALLocation two, dispatch varying + - P r i o r i t y one intersector, aLLocation varying 0 • ALLocation one, dispatch varying & - A L L intersector, aLLocation varying

- A L L o c a t i o n three, dispatch varying

Fig. 6

can be improved in some cases through the introduction of intersector dispatching. The cases are defined by the type of deployment in effect. Therefore, one can conclude that improvements of workload equity created by changing geographic allocatioin of patrol units seem to be greater than those caused by intersector dispatching policy.

C O N C L U S I O N

The introduction of intersector dispatching can have a dramatic effect on the average response time of a police patrol force. Marked reductions of response time have been illustrated for those deployments using intersector dispatching in this simulation study.

As mentioned earlier, several limitations were imposed upon the simulated patrol environment by this experiment. The geographic region used in the study was rather simple, and the varieties of travel routes caused by interse'ctor dispatching were limited. Future experiments should broaden the values assigned to these factors when gauging the effect of intersector dispatching.

The implementation of intersector dispatching by police patrol administrators de- serves further study. The implementation of this tactic may require revision of the current patrol managerial organization. It will need increased coordination and communication between sectors. New policies may be necessary to establish the chain of command for managing officers dispatched to other sectors. Officers who are presently expected to learn detailed information concerning their particular 'beat' may be expected to acquire such information for several contiguous sectors in anticipation of intersector dispatching. If these possible problems can be overcome, and if future study supports the conclusions of this experiment, intersector dispatching promises to provide significant improvement of police patrol performance.

R E F E R E N C E S

1. Baker M (1985) Cops. Simon and Shuster. 2. Chaiken JM and Dormant P (1975) Patrol car

allocation model: executive summary. Rand Report R- 1786/I-HUD/DOJ (September).

3. Chalken JM, Crabill T, Holliday L, Jaquett¢ D, Lawless M and Quade E (1975) Criminal justice models: an overview. Rand Report R-1859-DOJ (October).


4. Chelst K (1978) An algorithm for deploying a crime directed (tactical) patrol force. Mgmt Sci. 24(12), 1314-1327.

5. Fishman GS (t978) Grouping observations in digital simulation. Mgmt Sci. 24(5), 510-521.

6. Green L (1984) Multiple dispatch queueing model of police patrol operations. Mgmt Sci. 30 (6), 653-664.

7. Green L (1984) A queueing system for auxilliary servers. Mgmt Sci. 30(10), 1207-1216.

8. Kern GM (1986) A computer simulation model for the study of police patrol deployment. In Proceedings: Decision Sciences Institute National Meeting, Honolulu, Hawaii.

9. Kolesar PJ and Walker WE (1975) A simulation model of police patrol operations: program description. Rand Report R-1625/2-HUD / N YC.

10. Larson RC (1972) Urban Police Patrol Analysis. MIT Press, Cambridge, Massachusetts.

I1. Larson RC (1978) Police Deployment. Lexington Books, Lexington, Massachusetts.

12. Maxfield MG (1979) Service time, dispatch time, and demand for police services: helping more by serving less.

(July, 1980) Revised paper at the ORSA,rTIMS National Meeting (October).

13. McKnew MA (1983) An approximation to the hypercube model with patrol-initiated activities: an application to police. Decis. Sci.

14. Pritsker AAB (1979) Introduction to Simulation and SLAM. Halstead, New York.

15. Rubinstein J (1973) City Police. Ballantine Books, New York.

16. Saladin BA (1982) Goal programming applied to police patrol allocation. Working paper of the University of Georgia College of Business Administration.

17. Scott E (1981) Calls for Service, Citizen Demand, and Initial Police Response. National Institute of Justice.

18. Siegel S (1956) Nonparametric Statistics for the Behat,. ioral Sciences. McGraw-Hill, New York.

ADDRESS FOR CORRESPONDENCE: Gary M Kern, Department of Management, College of Business Administration, Uni- versity of Notre Dame, Notre Dame, Indiana 46556, USA.

OME. 15/2.~F

Documents

The effect of intersector dispatching on police patrol performance