Matriz de instrumento

Process models are discovered by finding causal relations between activities. We take the operators who perform resolution activities on the tickets as the activities in our log. So, the discovered process models from our log describe the relations among operators. That’s why we do not perform social network miner tool to discover social relations between operators.

Here we apply Casual Activity Matrix process mining tool to investigate the causal dependencies among operators in handling a certain type of category to find out more about the social structure among operators. This tool represents the causal relations between activities. Since in our log we have operator names as activities, this tool gives us the information of causal relations between operators. In this tool, the magnitude of the causal relation between any two activities are measured with a value which ranges from -1 to 1. A value of -1 in a cell of the causal activity matrix with rowAand column

B indicates that there is no causal relation fromAtoB, a value of 0 indicates that there is no evidence to confirm any relation fromAtoB, and a value of 1 indicates that there is a causal relation fromA toB.

The metric which is used to measure the strength of the causality dependency between two activities that is described in [30] is as follows.

Let a and b be two activities in a log L, let |a >L b| be the number of times that

activity a is followed by activity b inL, and let a⇒Lb denote the causal dependency

betweenaand b, then a⇒_Lb is defined by

a⇒Lb=

|a >Lb| − |b >La|

|a >Lb| − |b >La|+ 1

. (5.1)

In the colored representation of Causal Activity Matrix tool, if there is no relation found from the row activity to the column activity of a cell in the matrix, then the cell is colored with red, if there is no information about causal relation, then the cell is colored white and if there is found a casual relation, then the cell is colored blue. The closer a cell value gets to 1, it indicates stronger casual relation from the row activity to the column activity.

We discover causal relations among operators with causal activity matrix tool for ‘Laptop’ category tickets (see figure 5.11). This matrix shows causal relations between operators who are involved in resolving tickets of ‘Laptop’ category. In some cells of this matrix there are values between 0.5 and 0.75. For those cells, the value of the cell implies the strength of the causal relation from the operator in the row of the matrix to the operator in the column of the matrix. In the cases that there is a value which is close to 1 in a cell with row operator Oi and column operator Oj, causal relation measure

implies that tickets after being processed by Oi are likely to be routed to operatorOj.

6 Modelling Ticket Resolution Process

In this chapter, we present the queueing network model of the ticket resolution process, how we analyze the server structures with the help of process mining and data-drived model input parameters.

6.1 Process Insights

Our research aims to make use of process mining to gain insights of the ticket resolution process and to make use of the gained process insights to build the queueing network model of the ticket resolution process. From our log which contains operators as activi- ties, we define the life-cycle of a ticket as a path that is followed among operators. When a ticket is transferred from an operator to another operator, the ticket is delayed and we treat the delay as an activity that a ticket goes through when the ticket is transferred. Thus, the life-cycle of a ticket consists of the resolution services by operators on the ticket and the delays between the resolution services. Namely, a ticket is either being served by an operator or is being delayed from the time that the ticket is first created to the time that it is finally resolved. Therefore, we take operators and delay as servers in our queueing network model of the ticket resolution process. In figure 6.1, the life-cycle of a ticket which has three resolution services by operatorsO1,O2 andO3 is illustrated. The discovered process model of the ticket resolution process shows that the tickets do not follow structured paths among operators and there are no insights into which activities precede which activities. With this insight, in our queueing network model of the ticket resolution process we allow every possible routing between any two operators via delay server.

By filtering the log by ticket categories, we observe less number of operators who are involved in the resolution and more structured processes. We consider the ticket cate- gories as customer classes and define routing probabilities by categories in our queueing network model. t0 O1 t1 Delay t2 t3 O2 Delay t4 O3 t5

Operator1 Operator2 Operatorl

Delay

Figure 6.2: Queueing Network Model