# Analytical Model for Enhancing the Adoptability of Continuous Descent Approach at Airports
## 4 Model Development  
### Background on Queueing Theory  
In this subsection, we briefly discuss the fundamentals of queueing theory. Queues, or waiting lines, are common in people's daily lives. Queueing theory is the field of study within operations research (OR) that concerns the study of queueing models to represent the different types of queueing systems (systems that involve some sort of queue) that appear in real-world applications. Thus, these queueing models are helpful for determining how to operate a queuing system [42]. The basic process of most queueing models is that customers requiring service are generated over time by an input source (also known as a calling population). The arrival pattern by which customers are generated from the input source is statistically defined to accommodate the randomness of the customer arrival pattern. A common assumption is that customers arrive according to a Poisson process, that is, customers arrive at random but at a fixed mean rate, or equivalently, the time between consecutive customer arrivals, that is, interarrival time, follows an exponential distribution. These customers enter the queueing system and form a queue to wait for the required service. Queues could be infinite or finite according to the maximum permissible number of customers that they can contain. At certain times, a customer is selected from the queue for service according to some defined rule referred to as the queue discipline (usually first-come-first-serve, shortly known as FCFS, or some priority-based rule). The service is then provided to the selected customer by a service mechanism that may consist of one or more service facilities, each of which contains one or more servers. The time elapsed from the commencement to the completion of service for a customer is referred to as the service time. Collectively, characteristics of queueing systems include arrival patterns of customers, service patterns of server(s), the number of servers, system capacity, queuing discipline, and the number of service stages, if more than one service stage exists [43]. A convenient notation for summarizing the basic characteristics of the queueing systems was developed by [PERSON] and is known in the literature as the Kendall notation. It follows the notation of (a/b/c), where a = customer arrivals distribution, b = service time distribution, and c = number of servers [44]. For instance, the queuing model (M/D/5) uses Markovian (or Poisson) arrivals (or equivalently, exponential interarrival time distribution), deterministic (constant) service time, and five parallel servers. Generally, there are three basic measures of performance for queuing systems: the waiting time that a typical customer endures, the number of customers that may accumulate in the queue or system, and the idle time of the servers. Since most queuing systems follow random processes (i.e., stochastic processes), these measures are represented as random variables, and thus, their probability distributions need to be defined. Depending on if the main objective of modeling a queuing system is whether to determine some measure of effectiveness for a given process or to design the optimal system based on some defined criterion, the measures of performance could include the expected number of customers in the system, expected number of customers in the queue, expected waiting time in the system, expected waiting time in the queue, and expected number of busy servers. Beyond the previously mentioned measures of performance, there is a measure of performance of particular interest that indicates the percentage of time the service facility within the queuing system is being utilized. This measure of performance represents the traffic intensity or utilization factor, which is the expected arrival rate of the customers to the queuing system, divided by the expected service rate, assuming one server in the service facility. If more than one server is available, then the number of servers must be multiplied by the expected service time.