Introduction2QueueingTheory

# Introduction2QueueingTheory - CPE 619 Introduction to...

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CPE 619 Introduction to Queuing Theory Aleksandar Milenković The LaCASA Laboratory Electrical and Computer Engineering Department The University of Alabama in Huntsville http://www.ece.uah.edu/~milenka http://www.ece.uah.edu/~lacasa

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2 Overview Queueing Notation Rules for All Queues Little's Law Types of Stochastic Processes
3 Queueing Models: What Will You Learn? What are various types of queues? What is meant by an M/M/m/B/K queue? How to obtain response time, queue lengths, and server utilizations? How to represent a system using a network of several queues? How to analyze simple queueing networks? How to obtain bounds on the system performance using queueing models? How to obtain variance and other statistics on system performance? How to subdivide a large queueing network model and solve it?

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4 Basic Components of a Queue 1. Arrival process 6. Service discipline 2. Service time distribution 4. Waiting positions 3. Number of servers 5. Customer Population Example: students at a typical computer terminal room with a number of terminals. If all terminals are busy, the arriving students wait in a queue.
5 Kendall Notation A/S/m/B/K/SD A : Arrival process S : Service time distribution m : Number of servers B : Number of buffers (system capacity) K : Population size, and SD : Service discipline

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6 Arrival Process Arrival times: Interarrival times: τ j form a sequence of Independent and Identically Distributed (IID) random variables The most common arrival process: Poisson arrivals Inter-arrival times are exponential + IID Poisson arrivals Notation: M = Memoryless = Poisson E = Erlang H = Hyper-exponential G = General Results valid for all distributions
7 Service Time Distribution Time each student spends at the terminal Service times are IID Distribution: M, E, H, or G Device = Service center = Queue Buffer = Waiting positions

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8 Service Disciplines First-Come-First-Served (FCFS) Last-Come-First-Served (LCFS) Last-Come-First-Served with Preempt and Resume (LCFS-PR) Round-Robin (RR) with a fixed quantum. Small Quantum Processor Sharing (PS) Infinite Server: (IS) = fixed delay Shortest Processing Time first (SPT) Shortest Remaining Processing Time first (SRPT) Shortest Expected Processing Time first (SEPT) Shortest Expected Remaining Processing Time first (SERPT). Biggest-In-First-Served (BIFS) Loudest-Voice-First-Served (LVFS)
9 Common Distributions M : Exponential E k : Erlang with parameter k H k : Hyper-exponential with parameter k D : Deterministic constant G : General All Memoryless: Expected time to the next arrival is always 1/ λ regardless of the time since the last arrival Remembering the past history does not help

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10 Example: M/M/3/20/1500/FCFS Time between successive arrivals is exponentially distributed Service times are exponentially distributed
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Introduction2QueueingTheory - CPE 619 Introduction to...

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