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MTAT.03.231 Business Process Management Lecture 7 – Quantitative Process Analysis II Marlon Dumas marlon.dumas ät ut . ee 1
Process Analysis 2
Process Analysis Techniques Qualitative analysis Value-Added & Waste Analysis Root-Cause Analysis Pareto Analysis Issue Register Quantitative Analysis Flow analysis Queuing analysis Simulation 3
1. Introduction 2. Process Identification 3. Essential Process Modeling 4. Advanced Process Modeling 5. Process Discovery 6. Qualitative Process Analysis 7. Quantitative Process Analysis 8. Process Redesign 9. Process Automation 10.Process Intelligence 4
Flow analysis does not consider waiting times due to resource contention Queuing analysis and simulation address these limitations and have a broader applicability Why flow analysis is not enough? 5
Capacity problems are common and a key driver of process redesign Need to balance the cost of increased capacity against the gains of increased productivity and service Queuing and waiting time analysis is particularly important in service systems Large costs of waiting and/or lost sales due to waiting Prototype Example – ER at a Hospital Patients arrive by ambulance or by their own accord One doctor is always on duty More patients seeks help longer waiting times Question : Should another MD position be instated? Queuing Analysis © Laguna & Marklund 6
If arrivals are regular or sufficiently spaced apart, no queuing delay occurs Delay is Caused by Job Interference Deterministic traffic Variable but spaced apart traffic © Dimitri P. Bertsekas 7
Burstiness Causes Interference Queuing results from variability in processing times and/or interarrival intervals © Dimitri P. Bertsekas 8
Deterministic arrivals, variable job sizes Job Size Variation Causes Interference © Dimitri P. Bertsekas 9
The queuing probability increases as the load increases Utilization close to 100% is unsustainable too long queuing times High Utilization Exacerbates Interference © Dimitri P. Bertsekas 10
Common arrival assumption in many queuing and simulation models The times between arrivals are independent, identically distributed and exponential P (arrival < t) = 1 – e -λt Key property: The fact that a certain event has not happened tells us nothing about how long it will take before it happens e.g., P(X > 40 | X >= 30) = P (X > 10) The Poisson Process © Laguna & Marklund 11
Negative Exponential Distribution 12
Basic characteristics: l (mean arrival rate) = average number of arrivals per time unit m (mean service rate) = average number of jobs that can be handled by one server per time unit: c = number of servers Queuing theory: basic concepts arrivals waiting service l m c © Wil van der Aalst 13