越览（106）——精读期刊论文的5应急系统的大量应用（1）

摘要：This post will introduce the extensive application of emergency systems (1) of the journal article "Improving emergency responsive

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今天小编为大家带来“越览（106）——精读期刊论文

《Improving emergency responsiveness with

management science》的

5应急系统的大量应用（1）”。

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Today, the editor brings you the

＂Yue Lan (106)：Intensive reading of the journal article＇Improving emergency responsiveness with

management science:

5 Extensive application of emergency systems (1)＇＂.

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一、内容摘要（Summary of content）

本期推文将从思维导图、精读内容、知识补充三个方面介绍期刊论文《Improving emergency responsiveness with management science》的应急系统的大量应用（1）。

This post will introduce the extensive application of emergency systems (1) of the journal article "Improving emergency responsiveness with management science" from three aspects: mind mapping, intensive reading content, and knowledge supplement.

二、思维导图（Mind mapping）

三、精读内容（Intensive reading content）

本节概述了早期在《管理科学》上发表的一些关于紧急服务车辆调度和定位的具有实践影响力的研究。这些研究起源于纽约市的模拟工作，重点关注救护车的优化部署。讨论了如何通过优化模型确定紧急车辆（如消防车）的位置以最小化总平均响应时间。平方根模型广泛应用于RAND消防项目，用于优化消防车的分配和位置，减少响应时间。

This section provides an overview of some of the early and influential research published in Management Science on the dispatch and location of emergency service vehicles. These studies originated from simulation work in New York City, focusing on the optimal deployment of ambulances. It discusses how to determine the location of emergency vehicles (such as fire trucks) through optimization models to minimize the overall average response time. The square root model was widely used in the RAND fire protection project to optimize the allocation and location of fire trucks and reduce response times.

接着讨论了巡逻车分配模型（PCAM）。与传统的依赖主观加权平均的警察巡逻队分配方法不同，PCAM使用了M/M/c排队模型，并能够在描述性或规范性模式下运行。它提供了多项输出指标，如平均排队时间、行程时间、车辆利用率和预防性巡逻频率等。该模型还考虑了非服务性活动（如用餐、维修等），并允许对不同班次、区域以及巡逻长度进行调整，从而帮助警察管理人员优化资源分配。PCAM因其灵活性和实际应用价值，广泛应用于多个城市的巡逻分配中。

The patrol car assignment model (PCAM) is then discussed. Unlike traditional police patrol allocation methods that rely on subjective weighted averages, PCAM uses the M/M/c queuing model and can operate in descriptive or normative mode. It provides multiple output indicators, such as average queue time, travel time, vehicle utilization, and preventive patrol frequency. The model also takes into account non-service activities (such as meals, maintenance, etc.) and allows adjustments for different shifts, areas, and patrol lengths, thereby helping police managers optimize resource allocation. PCAM is widely used in patrol allocation in many cities due to its flexibility and practical application value.

PCAM最初使用纽约市的数据进行验证，并在1970年代的金融危机期间帮助做出削减巡逻资源的决定。随后，该模型被推广到美国40多个警察局、加拿大、荷兰以及以色列的警察部队。在大多数地方，PCAM通过本地数据验证后得以实施，并且其应用带来了运营上的变化。

PCAM was initially validated using data from New York City and helped make decisions to cut patrol resources during the financial crisis of the 1970s. The model was subsequently extended to more than 40 police departments in the United States, Canada, the Netherlands, and Israel. In most places, PCAM was implemented after being validated with local data, and its application led to operational changes.

四、知识补充（Knowledge supplement）

M/M/c排队模型是排队论中的一种经典模型，通常用于描述多个服务通道的排队系统。具体来说，M/M/c排队模型具有以下特点：

The M/M/c queuing model is a classic model in queuing theory, which is usually used to describe queuing systems with multiple service channels. Specifically, the M/M/c queuing model has the following characteristics:

M：到达过程遵循泊松过程，即顾客（或任务）的到达是完全随机的，并且到达间隔服从指数分布。到达率为λ（单位时间内顾客到达的平均数量）。

M: The arrival process follows a Poisson process, that is, the arrival of customers (or tasks) is completely random, and the arrival interval follows an exponential distribution. The arrival rate is λ (the average number of customers arriving per unit time).

M：服务过程也遵循泊松过程，即每个服务通道的服务时间服从指数分布。服务率为μ（单位时间内每个服务通道能够完成的服务数量）。

M: The service process also follows the Poisson process, that is, the service time of each service channel follows an exponential distribution. The service rate is μ (the number of services that can be completed by each service channel per unit time).

c：表示系统中服务通道的数量。也就是系统中有多少个服务器同时处理顾客（或任务）。c是一个正整数，表示服务员的数量。

c: represents the number of service channels in the system. That is, how many servers in the system handle customers (or tasks) at the same time. c is a positive integer, representing the number of waiters.

M/M/c模型常用于分析以下情况：

The M/M/c model is often used to analyze the following situations:

有多个服务窗口（例如，多个银行柜台、多个排队窗口等），客户排队等待服务。

There are multiple service windows (e.g., multiple bank counters, multiple queue windows, etc.), and customers queue up to wait for service.

顾客到达和服务时间都服从指数分布（即无记忆的随机过程）。

Customer arrival and service times are both exponentially distributed (i.e., memoryless random processes).

系统可以同时处理多个顾客（c个服务通道）。

The system can handle multiple customers (c service channels) simultaneously.

该模型通常用于计算系统的关键性能指标，例如排队长度、等待时间、系统中的顾客数量等，并且广泛应用于通信网络、呼叫中心、交通流量等领域。

This model is often used to calculate key performance indicators of the system, such as queue length, waiting time, number of customers in the system, etc., and is widely used in communication networks, call centers, traffic flow and other fields.

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