Kelly Rosa Braghetto

Ph.D. student at Department of Computer Science
Institute of Mathematics and Statistics
University of São Paulo

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Applying Performance Analysis Modeling into Business Processes Management (BPM) Domain

Results of Some Experiments

Applied Formalisms		Correspondent Supporting Tool
Generalized Stochastic Petri Nets (GSPN)	⇒	Simulation and Markovian Analyzer for Reliability and Timing (SMART)
Performance Evaluation Process Algebra (PEPA)	⇒	PEPA Plug-in Project
Stochastic Automata Networks (SAN)	⇒	Performance Evaluation of Parallel Programs (PEPS)

Modeling Scenarios

Each scenario, by means of a simple model example, covers some important aspect in the modeling of business processes and evidences the pros and cons of the studied formalisms.

• Scenario 1: Basic Structures
• Scenario 2: Advanced Branching / Merging Structures
• Scenario 3: Functional Dependencies

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Scenario 1: Basic Structures

Example of a typical "Order Processing" business process

BPMN Model

GSPN Model

( Source file of the GSPN model for SMART   ⇒   example1.sm )

Timed transitions	ta	tb	tc	td	te	tf	tg	th	ti	tj	tk	tl	tm
Rate	0.33	0.20	1.00	0.50	0.07	1.00	0.50	0.01	0.50	1.00	0.50	1.00	1.00

Immediate transitions	prob(c)	prob(d)	prob(e)	prob(g)	prob(k)	prob(l)
Probabilities	0.10	0.90	0.25	0.75	0.05	0.95

PEPA Model

Source file of the PEPA model for the PEPA Plug-in Project   ⇒   example1.pepa )

 
// Execution rates associated to each activity
rate_a = 0.33;   rate_b = 0.20;   rate_c = 1.00;
rate_d = 0.50;   rate_e = 0.07;   rate_f = 1.00;
rate_g = 0.50;   rate_h = 0.01;   rate_i = 0.50;
rate_j = 1.00;   rate_k = 0.50;   rate_l = 1.00;
rate_m = 1.00; 

// Routing probabilities associated to the choices
prob_c = 0.1;	prob_d = 1 - prob_c;
prob_e = 0.25;	prob_g = 1 - prob_e;
prob_k = 0.05;	prob_l = 1 - prob_k;

// Number of servers
num_servers = 1;

// Order processing
POrderProcessing = (a, rate_a).((b, prob_c * rate_b).(c, rate_c).POrderProcessing +  
                                (b, prob_d * rate_b).PStock);
PStock           = (d, prob_g * rate_d).PFinalize + 
                   (d, prob_e * rate_d).(e, rate_e).(f, rate_f).PFinalize; 
PFinalize        = (g, rate_g).(h, rate_h).(m, rate_m).POrderProcessing;
PInvoice         = (g, infty).(i, rate_i).PCheck;
PCheck           = (j, prob_l * rate_j).(l, rate_l).(m, infty).PInvoice + 
                   (j, prob_k * rate_j).(k, rate_k).PCheck;

// Whole process
POrderProcessing[num_servers] <g,m> PInvoice[num_servers]
		

SAN Model

( Source file of the SAN model for PEPS   ⇒   example1.san )

Event Type Rate a loc 0.33 b1 loc prob(d) * 0.20 b2 loc prob(c) * 0.20 c loc 1.00 d1 loc prob(e) * 0.50 d2 loc prob(g) * 0.50 e loc 0.07 f loc 1.00 g sync 0.50 h loc 0.01 i loc 0.50 j1 loc prob(k) * 1.00 j2 loc prob(l) * 1.00 k loc 0.50 l loc 1.00 m sync 1.00

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Scenario 2: Advanced Branching / Merging Structures

A simple model of a process to determine the cost of a medical service (based on the french health-care system)

BPMN Model

GSPN Model

( Source file of the GSPN model for SMART   ⇒   example2.sm )

Timed transitions ta tb tc td te Rate 0.50 0.20 0.25 0.01 1.00 Immediate transitions prob(b) 1 - prob(b) prob(d) 1 - prob(d) Probabilities 0.85 0.15 0.73 0.27

PEPA Model

( Source file of the PEPA model for the PEPA Plug-in Project   ⇒   example2.pepa )

 
// Execution rates associated to each activity
r_a = 0.50; r_b = 0.20; r_c = 0.25; r_d = 0.01;
r_e = 1.00; r_immediate = 50.00;

// Routing probabilities associated to the multi-choice
prob_c = 0.85; prob_d = 0.73;

// Medical service cost calculation sub processes
PCalc = (a,r_a).(b,r_b).(e,r_e).PCalc;  
P1    = (b,infty).((c1,prob_c * r_immediate).(c,r_c).(e, infty).P1 +
                   (c2,(1-prob_c) * r_immediate).(e,infty).P1);
P2    = (b,infty).((d1,prob_d * r_immediate).(d,r_d).(e,infty).P2 +
                   (d2,(1-prob_d) * r_immediate).(e,infty).P2);

// Whole process
PCalc <b,e> P1 <b,e> P2
			

SAN Model

( Source file of the SAN model for PEPS   ⇒   example2.san )

Event Type Rate a loc 0.50 b sync 0.20 c1 loc prob(c) * 50 c2 loc (1 - prob(c)) * 50 c loc 0.25 d1 loc prob(d) * 50 d2 loc (1 - prob(d)) *50 d loc 0.01 e sync 1.00

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Scenario 3: Functional Dependencies

A simple "producer / packer" process

BPMN Model

GSPN Model

( Source file of the GSPN model for SMART   ⇒   example3.sm )

Timed transitions ta tb tc td Rate 0.02 0.10 0.33 0.12

PEPA Model

( Source file of the PEPA model for the PEPA Plug-in Project   ⇒   example3.pepa )

 
// Execution rates associated to each activity
rate_a = 0.02;  rate_b = 0.1; 
rate_c = 0.33;  rate_d = 0.12;

// Sub processes representing the producer and the packer
PProducer = (a, rate_a).(b, rate_b).PProducer;
PPacker    = (c, rate_c).(d, rate_d).PPacker;

// Sub process representing a stock with max size = 9 
PStock  = (a,infty).(b, infty).PStock1;
PStock1 = (a,infty).(b, infty).PStock2;
PStock2 = (a,infty).(b, infty).PStock3;
PStock3 = (a,infty).(b, infty).PStock4 + (c, infty).PStock;
PStock4 = (a,infty).(b, infty).PStock5 + (c, infty).PStock1;
PStock5 = (a,infty).(b, infty).PStock6 + (c, infty).PStock2;
PStock6 = (a,infty).(b, infty).PStock7 + (c, infty).PStock3;
PStock7 = (a,infty).(b, infty).PStock8 + (c, infty).PStock4;
PStock8 = (a,infty).(b, infty).PStock9 + (c, infty).PStock5;
PStock9 = (c,infty).PStock6;

// Whole process
PProducer <a,b> PStock <c> PPacker 
			

SAN Model

( Source file of the SAN model for PEPS   ⇒   example3.san )

Event Type Rate a loc f b sync 0.10 c syn 0.33 d loc 0.12 f = 0.00,    if state(A3) == 3_9 0.02,    if state(A3) != 3_9