City streets parking enforcement inspection decisions: The Chinese postman’s perspective

Highlights

• We view an administrative activity of issuing parking tickets in a city street setting as a revenue collection activity.

• The task of designing parking permit inspection routes is modeled as a revenue collecting Chinese Postman Problem.

• We demonstrate that our design of inspection routes maximizes the expected revenue.

• We investigate decision rules that allow the officers to adjust online their routes in response to the parking permits’ times.

• Our simulation shows that allowing an officer to selectively wait by cars until permit expires increases expected revenues between 10–69 percent.

Abstract

We view an administrative activity of issuing parking tickets in a dense city street setting, like downtown Philadelphia or NYC, as a revenue collection activity. The task of designing parking permit inspection routes is modeled as a revenue collecting Chinese Postman Problem. After demonstrating that our design of inspection routes maximizes the expected revenue we investigate decision rules that allow the officers to adjust online their inspection routes in response to the observed parking permits’ times. A simple simulation study tests the sensitivity of expected revenues with respect to the problem’s parameters and underscores the main conclusion that allowing an officer to selectively wait by parked cars for the expiration of the cars’ permits increases the expected revenues between 10% and 69 percent.

Introduction

Consider a large city street grid, like downtown Philadelphia or New York City, represented as a graph G = (V, E), with parking segments along some streets in G and the common/familiar parking kiosk setting where the car owners buy parking time and place the receipt/permit on the dashboard of the car. The city administrators would like to maximize their street parking revenues by (a) collecting the parking fees from the legally parked cars – cars parked in designated parking spaces conforming to the parking times they purchased, and by (b) issuing parking tickets to cars parked in violation of the parking rules. Violation of the parking rules can take a number of forms. In our inquiry, we restrict the analysis to the time violations with respect to the parking times the car owners purchased and the parking tickets issued by the parking enforcement officers when observing parking time violations.

In order to collect the revenues from the parking violations, the city administrators usually resort to employing a crew of enforcement officers assigned to patrol the city parking areas at any given time of day and night. Consider a single parking enforcement officer’s assignment. Without inferring any gender bias, we refer to the parking enforcement officer (from now on referred to as PEO) by the generic ‘he’. As such, the officer is usually assigned a subgraph of city streets, say G′(V′, E′)⊂G, and he has to select (or is provided) an itinerary that traverses all the edges (it is edges since the PEO can traverse a street segment in either direction using the sidewalk) in G′ where paid parking is allowed. We assume for simplicity that the subgraph G′ is a connected component of G and all edges of E′ have to be regularly inspected by the PEO during his patrol, both for public safety reasons and for the main function of parking permit enforcement. Again, the edges in E′ correspond to the segments of the streets along which paid parking is allowed. The PEO inspects the cars’ parking permits by walking along streets’ sidewalks. Since a PEO can walk on any sidewalk in either direction the graphs G and G′ are considered to be undirected. If paid parking is allowed on both sides of a given street segment the graph G′ is a multigraph with two edges connecting the corresponding pair of nodes in V′. From now on we will refer to G′ as a multigraph. In case it is desired to inspect the edges of the undirected multigraph G′ with different frequencies, we add without loss of generality appropriate copies of these edges to G′. The PEO does not know in advance the number, density, and individual parking times purchased for the parked cars. As he traverses the multigraph G′, he has to decide how, in what order of street segments (edges in G′), to traverse the streets’ segments and at what rate; should he stop and wait next to a car whose parking time on the permit is about to expire or continue to the next car? Essentially, at each car a PEO has an option to wait, return to previously inspected cars, or continue walking to inspect the ‘next’ car. It corresponds to processing parking cars’ information in real time and represents a real-time (online) optimization problem with the objective of collecting the maximum expected revenues from a PEO’s patrol assignment. At least that would be one of a number of the city administrators’ objectives to consider.

Optimizing the traversal order of a multigraph’s edges is not a new problem. Given a connected multigraph G′(V′, E′) with ‘length’ weights w(e) for each edge e ∈ E′, the problem of designing the shortest tour – a path or a circuit, that traverses each edge in E′ at least once is well known under the heading of the Chinese Postman Problem (CPP) and dates back to 1962 (http://www.nist.gov/dads/HTML/chinesePostman.html ).

In our problem of designing a traversal scheme for a single PEO, we need to define a few more concepts. We associate with each edge e in the street multigraph G′ three weights; the weight w(e) expresses the expected revenue collected from edge e ∈ G′, $\widehat{w}\left(e\right)$ represents the expected traversal time of edge e while inspecting the cars parking permits, and w (e) is the dead-heading time for e (the traversal time with no inspections). The traversal minimization CPP problem on G′ refers to the weights $\widehat{w}\left(e\right)$ and dead-heading weights w (e). Our parking ticket revenue management problem is defined more formally below. Note that dead-heading edges might have to be added to E′ when solving a CPP on G′ as a necessary part of the CPP solution. We assume for now that in a planar graph such as a city street graph, we can construct an optimal CPP solution that traverses an edge in a dead-heading mode, when it is required, immediately after traversing it in a ‘working’ mode. We revisit this assumption in the paper’s Summary section. Observe that with the assumption of triangle inequality time traversal matrix for G′ for both ‘working’ mode times and dead-heading times, in an optimal CPP solution any edge in G′ will have at most one dead-heading traversal.

Motivation: The potential of increased revenues due to more efficient issuing of parking tickets may constitute a non-negligible contribution to social economic well-being for many cities. Cities like New York, Philadelphia, Chicago, etc., are in great need for revenues and are desperately searching for innovative ways to raise additional revenues. The basic concept of CPP for an efficient traversal of city streets is well known to municipal managers from, for instance, planning of garbage collection operations (Beltrami and Bodin, 1974). Implementing some of the findings of this study in the daily routine operation of PEOs is rather straightforward.

The solution presented in this paper has the potential to increase revenue by about 10–69 percent. The significance of increasing parking ticket revenues by even 10 percent is invaluable for any city. Quoting from one source on parking fines (http://money.cnn.com/2004/05/03/news/parkingfinesup/ ): “A typical fine in Manhattan now can make your wallet $65 lighter. Parking at a fire hydrant or bus stop will run $115. The city’s parking violations bureau expects to collect $562 million this year, up 48 percent from 2002. Los Angeles will collect $110 million in 2004, up 20 percent from two years ago. Angelenos endure some of the highest fines in the country; parking illegally in a disabled persons zone can draw a whopping $355 fine. Another beneficiary of higher parking fines is Chicago. Revenue has climbed 28 percent from 2002 to $141 million.”

The significance of increasing parking related revenues can be illustrated by considering the city of Pittsburgh with population of about 0.3 million (http://www.census.gov/newsroom/releases/archives/2010_census/cb11-cn74.html ). Based on the information from http://www.city.pittsburgh.pa.us/pghparkingauthority/assets/09_PPA_Annual_Report.pdf and http://www.post-gazette.com/pg/11248/1172336-53-0.stm?cmpid=localstate.xml , the total revenue of Pittsburgh Parking Authority from parking permit purchases and parking ticket revenues was $42 million. The city issued 280,000 tickets. The parking authority collected about $5 million from all parking-related fines with $2 million from expired meter fines. In terms of ticket-related variable cost, the facility and parking court management expenses were only $2 million (i.e. the variable cost is only 40 percent of all fines revenue). If we scale the number to match large cities, e.g. Manhattan, the 10 percent increase would translate to several million dollars.

In 2003, the city of Berkeley collected $6.9 million from parking citations, out of this amount, $2.3 million was attributed to tickets issued for expired meters (http://www.berkeleydailyplanet.com/article.cfm?archiveDate=05-14-04&storyID=18852 ). In 2009, the city of Milwaukee issued nearly 150,000 tickets for expired meters which would have brought in $3.3 million if all the tickets were paid (http://www.bizjournals.com/milwaukee/print-edition/2011/01/07/expired-downtown-parking-meters.html?page=all ). In terms of cost information, citing the Seattle Parking Management Study of September 2002 (96 page report), “The parking ticket revenue generated by a Parking Enforcement Officer (PEO) is approximately three times the cost of labor and necessary equipment. ... the average PEO generates $240 per hour in ticket revenue (collected revenue), ...”.

The outline of this paper is as follows: Section 2 discusses the structure of our problem relative to other problems examined within Operational Research. Section 3 describes our notation and introduces the problem of designing a PEO route over G′ as a CPP. In Section 3.1 we start with the analysis of local inspection decisions regarding which car to inspect next as a function of the remaining times for the cars inspected so far on a given street segment. We begin by considering an option of waiting in front of a parked car with a valid permit anticipating its permit to expire before its owner’s arrival. We denote this option as memory size = 1. This operational option can be extended by allowing to step back to the last previously inspected car (memory size = 2). The general case of allowing to step back to any previously inspected car or just inspecting a new car is examined in Section 3.1.3. A simple simulation study for the CPP routing with inspections with online local decisions is presented in Section 4. In Section 5 we present the results. In the summary and discussion sections (Section 6) we examine the related technological issues and the feasibility of implementation.