**1. Introduction**

In an elevator traffic system within a building, the origin-destination matrix is a compact-concise tool that is used to clearly describe the probability of a passenger travelling from one floor in the building to another. It is a two-dimensional square matrix. The diagonal elements of the matrix are equal to zero, since rational passenger behaviour is assumed (i.e. no passengers will travel from a floor to the same floor). Moreover, the sum of all the elements within the matrix is equal to one (representing the universal set in probability). The row index of the matrix denotes the origin floor of the passenger's journey, whilst the column row denotes the destination floor of the passenger's journey.

It is worth noting that all the events in the *OD* matrix are mutually exclusive (i.e., if one of them takes place in a round trip, the others cannot take place in the same round trip). As an example, if a passenger chooses to go from the third floor to the seventh floor in a round trip, he/she cannot also go from the eighth floor to the second floor in the same round trip.

The general format for an *OD* matrix is shown below. All the diagonal elements are equal to zero, as it is assumed that passengers are rational and would not travel from a floor to the same floor.

$$OD\_{adj} = \begin{bmatrix} \mathbf{0} & p\_{1:2} & \dots & \dots & p\_{1:N-1} & p\_{1:N} \\ p\_{2:1} & \mathbf{0} & \dots & \dots & p\_{2:N-1} & p\_{2:N} \\ \dots & \dots & \dots & \dots & \dots & \dots \\ \dots & \dots & \dots & \dots & \dots & \dots \\ p\_{N-1:1} & p\_{N-1:2} & \dots & \dots & \mathbf{0} & p\_{N-1:N} \\ p\_{N:1} & p\_{N:2} & \dots & \dots & p\_{N:N-1} & \mathbf{0} \end{bmatrix}$$

The origin-destination matrix is critical for the elevator traffic design process, specifically for the following two functions:


The final origin-destination matrix must obey a number of rules, listed below:

1.The sum of all the elements in the *OD* matrix should add up to 1.

2.All the elements of the diagonal of the matrix should be equal to 0.

It is worth noting that work has been carried out in trying to estimate the origindestination traffic from elevator movements in the building [2–5]. The outcome can be used in a number of ways, including generating virtual passenger traffic [6] or deciding on the suitable group control algorithm to adopt during that period of time [7].

Previous work has shown how the origin destination matrix can be derived [8, 9]. However, those two pieces of work have assumed that any floor must either be an entrance floor or an occupant floor, but not both. The work presented in this paper relaxes this requirement and allows any floor to be both an entrance floor and an occupant floor.

Examples of traffic mix conditions that are believed to be representative of the lunch-time peak traffic conditions in many modern office buildings include: 40%:40%:20% [10]; 45%:45%:10% [11]; 42%, 42%, 16% [12]; incoming, outgoing and inter-floor traffic, respectively.

In addition, it is possible to calculate the round-trip time for general traffic conditions under the Poisson arrival process assumption [13, 14] or the plentifulpassenger-supply assumption [15, 16].

#### *A Universal Methodology for Generating Elevator Passenger Origin-Destination Pairs… DOI: http://dx.doi.org/10.5772/intechopen.93332*

This framework can then be combined with other design methodologies in order to be used as a comprehensive universal elevator traffic system design tool, whereby the average passenger waiting time and the average passenger travelling times can also be added as user requirements, and outputs such as the car capacity, the elevator speeds can be provided as outputs of the design.

Existing software packages [17] employ a slightly different method for generating passenger origin-destination pairs, which leads to marginally different results.

Section 2 describes the two types of floors. Section 3 describes the possible modes of traffic in a building. Section 4 describes how the traffic can be described in a building. Section 5 shows how the universal origin destination matrix can be derived. A numerical example is given in Section 6. Section 7 discusses the issue of verification to ensure the correctness of the final OD matrix. Conclusions are drawn in Section 8.
