Introduction

In the current world where the resources are being shared among different organization through the cloud computing paradigm, most of the organizations have started to shift towards Shared Business Process Management Infrastructure (SBPMI). Due to this shift in modelling paradigm, organizations have to continuously improve their process [1]. But most of the organizations are still depending on the external service providers to monitor their business process, hence the business links are to be established with those external agencies [2]. This issue was well addressed by the Information Technology by developing various work-flow tools [3] [4] [5] [6]. The challenge here is to extend the service from boundary of single organization to cross organizations.

Due to data explosion [7] getting insight and performing analysis on the data to understand their behaviour and discover an optimized process model is always been a challenge to any organization in the process mining environment. α y M iner uses SBPMI, to analyse the data behaviour of an organization. This is achieved by comparing the model of same variant using RBA M iner in SBPMI and recommending the best suitable process model. The context of this paper is the CoSeLoG Project2 . The data used for the experiment and analysis of proposed algorithm is obtained from the Configurable Services for Local Government (CoSeLoG) Project. This project was executed under Dutch Organization for Scientific Research (NWO) [8].

α y M iner is a new analytical tool for discovering the optimal path of completion of a partial trace along with recommendation of complete process model.

It proposes two novel techniques α y Comp and RBA M iner . α y Comp identifies the optimal path of completion by matching the partial trace and discovering the variants in all process models logged in the repository. It identify and recommends the Next Probable Activity (NPA) of partial trace. RBA M iner identifies the suitable resource for performing the discovered NPA, by analysing the behaviour of all resources capable of performing NPA based on their performance, load and waiting time.

α y M iner is analysed using the running example [2]. NPA for the partial trace and optimal process model is identified in cross organization environment using α y Comp [3] and the resource preferable for performing NPA is analysed and recommended using RBA M iner [4]. The experiment is conducted using the real time event log of CoSeLoG Project3 and the result of RBA M iner is presented in section [5].

Running Example

The proposed α y M iner is illustrated using the running example of four variant process model containing 9 activities, shown in Figure [1b]. The corresponding sample event log describing the process execution of the process model is shown in Table [1]. Here the traces matches model perfectly which is not the cases in real life process model. The complete log file of the running example can be found at Process Mining @ NITK4 . The experimental results are obtained using the CoSeLoG Project5 .

Proposed Problem

Consider an online process shown in Figure [ α y M iner is intended to identify and predict the optimal path of execution along with the complete process model, for a real time process. On identifying the currently executing activity A i , α y M iner recommends the optimal path of completion and the best suitable process model matching the partial trace with same variant event logs, logged in the process model repository. On identifying the matched variants, the optimal process models are identified by running process model comparator α y Comp which matches the partial trace. Recommendation of Next probable Activity NPA is done by selecting NPA (A i ) in identified suitable process model. The Algorithm [1] gives the execution steps of α y M iner. i.e., L ∈ A * and Let A be a th i activity and B be a th i+1 then,

Case ID TRACEḊirectlyF ollow (a> L b) ← {iff ∃ trace σ = t 1 , t 2 , ..., t n ∧ i ∈ [1, 2, ....., n − 1] | σ ∈ L, ∧ t i = a, ∧ t i + 1 = b}(1)Ċasuality (a−→ L b) ← {iff a > L b ∧ b ≯ L a} (2) U nrelated (a# L b) ← {iff a ≯ L b ∧ b ≯ L a} (3) Ṗ arallel (a L b) ← {iff a > L b ∧ b > L a}(4)Loop (a> L b> L a) ← {iff (a i == a i+2 ) → a i > L a i+1 > L a i+2 }(5)

The Table 2b gives the relation metric of all the four models in running example.

Complexity Metric Complexity metric identifies the joins and splits in the process model. Joins and split are identified using the result of output and input binding. Consider the Figure [1b] where for process model 1: O(A)={B}=85 times, similarly the split {CDE} = 20, its means 20 times activity C is 20 times followed by both D and E, join {GEH} is joined 16 times. Using this information complexity metric shown in Table[2c] is developed.

Service Time Metric This metric gives the total service time comparison for an activity in each model. This comparison helps in identifying the model serving an activity with less service time. The service time is calculated by each cases i=1 duration(A i ), where A i ⊆ A (set of activities). The sample output in seconds is shown in Table 2d.

Fitness Metric This gives the numbers of traces that can be successfully run on the model. This is helpful in deciding how efficient the model is, in running the trace. α y Comp identifies the model which runs maximum number of traces with minimum time. Consider the Table 2e.

Binding Relation

On identifying variants following the partial trace, the NPA of currently executing activity A i is identified using binding relation which bind the incoming and outgoing activity of A i . Algorithm 3 eplain the concept of binding relation, where for each trace in a case, if an activity A is followed by B, then A.outbond ← B ∧ B.inbound ← A, i.e., A has out-bounding relationship with B and similarly B as in-bounding relationship with A

if (|a > L b|) then 4 a.Outbound ← b ∧ b.Inbound ← a 5 |a > L b| = σ∈L L(σ) × |{1 ≤ i < |σ| | σ(i) = a ∧ σ(i + 1) = b}| [see [7]]

6 until for each sequence in trace σ in event log L 4 Resource Behaviour Analyser (RBA M iner ) α y M iner on discovering suitable process model with NPA identifies the resources preferable for performing NPA. Set of resource preferable for performing NPA is identified using Activity/Resource rep [3]. RBA M iner analyse the behaviour and recommend the suitable resource for performing NPA. Behaviour of the resources is analysed based on 3 parameter: Performance, Load and Queue using polynomial regression model for load and performance [4.2] and Average Servicing Time at resource using queue model [4.3]. Algorithm 4 explains the concept of resource behaviour analysis.

Activity/Resource rep

α y M iner identifies the list of resources performing an activity in entire process log along with the time consumed by them for performing that activity. The Table 3 gives representational view of list of resources performing an activity in process model 1 along with the time consumed. 6 until (for each resource of N P A in BestRes Activity Table ) 7 Recommend the optimal load, performance and waiting time resource

Resource load & performance analyser

The Yerkes-Dodson Law of Arousal, also known as Arousal Theory, states that by increasing arousal, the workers performance can be improved. However, if the level of arousal increases too much, performance decreases Figure [4a] [9]. The RBA M iner identifies the level of arousal : Optimal Load i.e., the maximum load the resource can handle efficiently, along with its performance using polynomial regression model. Performance is a ratio of Total time taken by Load. The performance was analysed by increasing the load and observing the time taken.

It was observed that, as the load was increased, the consumption of the time was decreasing. But at some point there was a drift and the time consumption started increasing. That drifted point is known as Arousal (optimal load and performance of the resources). The Algorithm [5] identifies the load and performance [T otal time ÷ ] for /resource/unit time.

The RBA M iner first filters the unperformed load 1 (an activity with 0 ms) and residual load 2 (an activities with exceptional duration). Then the actual load ( ) and average time of Service (α) of each worker each month is identified. Polynomial regression model [5] is applied on this cleaned data. Since the RBA M iner is intended in identifying the second degree regression model, the regression model initialize a 3×3 matrix (A) and 3×1 matrix (B) as shown in figure [4b& 4c]. Then the transpose of matrix A is multiplied with matrix B. The result obtained is the coefficient of polynomial equation. On applying the load on an equation the polynomial curve (power curve) is obtained as shown in figure. On analysing the polynomial curve and applying the Yerkes-Dodson Law the optimal load and optimal performance of a resource is identified for each month. 6until ((i=0 to 3) ∧ j=0)

Perfromance Load Optimal Load Optimal Performance (a) Yerkes Dodson Law A =      n n 1 n 1 2 n 1 n 1 2 n 1 3 n 1 2 n 1 3 n 1 4      (b) Matrix Table A B =      n 1 α n 1 (α× ) n 1 (α× 2 )      (c) Matrix Table B7

Polynomial Equation : β0 + β1 + β2 2 8 until (for each resource each unit time)

Activity Servicing Time Model

Along with identification of load and performance of the resource preferable for performing NPA, RBA M iner also finds the Activity Servicing Time (i.e., the average waiting time for an activity to be served by a resource), before that resource is recommended. Since the interest is in finding the queue at each resource, RBA M iner uses Single-Server Models (M/M/1):(GD/∞/∞) and (M/M/1):(GD/N/∞). Here the model (M/M/1):(GD/∞/∞) describe (Arrival 1 / Departure 2 / Server 3 ):(Queue discipline 4 / Max number in Queue 5 / Source of Calling 6 ).

Arrival 1 (λ) is the rate at which the activities are arrived at each resources and Departure 2 (µ) is the rate at which the arrived activities are served. Since RBA M iner is intended in identifying the average waiting time at each resource, the single server model is applied. When data was analyzed for First Come First Serve FCFS, Last Come First Serve LCFS and Service in Random Order SIRO, it was understood that arrival of the activity was following General Discipline GD as its Queue Discipline 4 . As the number in queue and source of calling is not defined RBA M iner marks them as infinity. The average waiting time in the system W s is identified using Equations [6][7][8][9]. The Algorithm Activity Servicing Time [6] starts with identifying the arrival rate λ and the servicing rate µ at each resources.

The λ n & µ n in generalized model is shown in Equation [6]. The traffic ρ: number of activities arriving and getting served per unit time is shown in Equation [7]. Hence the Average waiting time in system L s is given in Equation [9].

λ n = λ µ n = µ

Where n = 0,1,2....

(6) ρ = λ µ(7)W s = L s λ (8) L s = ρ 1 − ρ(93 else ⊥ = (( .∂) − ((Π − .Dt) × 24hrs × 60Sec)) Π × 24 × 60 µ( F iltered Year Month + ⊥) ←− µ( F iltered Year Month + ⊥) + 1;

4 Average Servicing Time in system ← Equation [6 to 9]

Experimental Analysis and Result

The α y M iner algorithm is evaluated by running it on CoSeLoG Project6 . The experiments Exp N P A , Exp AST and Exp L&P was performed on the CoSeLoG Municipality 2, which contains 645 cases and 376 activities. Experiments were conducted and analysed on set of every 100 cases. α y M iner makes 4 assumption:

Any activity whose duration is recorded as 0 millisecond is considered as never been executed, since the nanosecond time is not recorded, vocabulary of an activity is not taken into account [1], don't deal with Live or Dead locks and assume that all process have same starting activity.

Design of Experiment

The α y M iner experimental set up is shown in Figure [5]. Where the log is first cleaned and initialized using initializer from which the NPA is identified. Optimal resource for performing NPA is identified and their behaviour is analysed. Finally α y M iner recommends the best process and resource model. Experiment was simulated in the form of supervised learning, where the test Exp N P A was conducted for every 100 cases and starting from 2 nd activity of the sequence. Exp N P A was analysed by comparing it with the actual path of execution. The result of this comparison is shown un Figure [6] and on analysis it is studied that the percentage of error rate (marked by green line) in recommendation is lesser in later positions of execution when compared to earlier positions. The Exp N P A achieved 72.8568% of efficiency. On analysing the graph, it is understood that the behaviour of recommended path is always below the actual path of execution. Inclination shows the huge difference of behaviour between the actual and recommended path. For the cases 400 to 500, it is observed that the graph don't have red line, as the path of execution is critical and was observed to take optimal time for completion. Hence this proves that α y M iner, don't recommend if the path of execution is observed to be optimal.

Recommendation of Resource capable for performing NPA:

Exp AST

The Exp AST for each resource performing NPA. Waiting time of recommended resource was compared with the actual resource and it was studied that their performance was improved by 59.7303%. The Figure [7] The result of Exp L&P is shown in Table [5] and the Figure [8] shows the polynomial curve. Using the law of Arousal, the optimal load and performance at each resource can be identified. This result is used in making appropriate decision about resource behaviour and load assignments. Using the outcome of experiment proper recommendations can be made, whether to assign the task to that resource ot not. α y M iner provided a solution for recommending an optimal path of execution:

NPA along with the complete process model and resource preferable for performing NPA. α y M iner is a analytical tool which gave solution for real time business process execution, by analysing the process and resource behaviour. The Experimental result shows 72% of optimization in process execution and 59% improvement in the behaviour of resource based on their Average waiting time, load and performance. α y M iner was successful in recommending appropriate process and resource model for the real time process.