Office hours: Wednesday 1.30  3.00 only by appointment.
Exam  summer session
The next written text is on June 4, 2019, at 10.30, room P2.
(The results of the first and second midterm are available at the MidtermResults page.)
Results of the written exam held on January 10: RisultatiPrimoAppelloPCN19
Results of the February exam: RisultatiFebbraioPCN19
Results of July 2019: RisultatiSecondoAppello
Results of September 2019: RisultatiAppelloSettembre
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If you are interested in doing your thesis in any field related to computer network performance, algorithms and protocols,
here you can find a (non exhaustive) list of opportunities: thesis opportunities.
These thesis will potentially open the path to future research collaborations, research contracts and PhD studies, while giving you a perspective on new challenging topics in future technologies.
Day  Topics covered 
September 26, 2018  Introduction to the study of performance of computer systems. Motivating examples. Single server network (interarrival time, service time, service rate). Performance metrics: Response time, Waiting time, Population. Stability condition. From textbook: pages 316 + assignment ex 2.1. 
September 28, 2018  Discussion on ex 2.1. Performance metrics: throughput and utilization, discussion on user/provider's perspective. Probability review: Sample space, events and related probability. Conditional probability. Independent events. Law of total probability, Bayes law. Examples and excercizes in class. From textbook: pages 3137 + ex 2.1. 
October 3, 2018  Probability review: Discrete and continuous random variables. Probability mass and cumulative distribution function of discrete random variables. Common discrete distributions: Bernoulli, Binomial, Geometric and Poisson. Probability density and cumulative distribution function of continuous random variables. Common continuous distributions: uniform and exponential. Examples of probability distributions in computer networks: Poissonian arrivals, exponential interarrival and service times. Examples of geometric distribution in probabilistic routing. Expectation and conditional expectation. Utilization law: general case and single server, infinite queue case. Use of the total probability law to derive the utilization law. From textbook: pages 1620, 3747 + ex 3.1, 3.2. 
October 5, 2018  Probability review: Joint probability mass(discrete)/density(continuous) function Expectation of the sum and of the product of two random variables Which exponential happens first? Performance metrics: slowdown of a job Characterization of a closed network and related performance parameters: a discussion on the throughput of a batch system From textbook: pages 4757 + ex 2.2, 3.14, 3.5. 
October 10, 2018  Review of ex. 2.2. Ergodic systems (irreducible, positive recurrent, aperiodic systems). Little's law for open and closed systems (proof). Corollaries of Little's law: utilization law. Simple exercizes of Little's law application. Examples of systems with multiple devices and probabilistic routing, use of Little's law in a finite queue system with loss. From textbook: pages 95106 + ex 6.1, 6.2 
October 12, 2018  Operational laws: forced flow law, demand definition and demand law, bottleneck law, and related proofs. Examples of application of the operational laws to closed systems From textbook: pages 106111 + ex 6.5 
October 17, 2018  Review of operational laws. Whatif analysis of closed systems: performance bound theorem. Plot of performance bounds for throughput and response time. Population knee point. Examples of use of bounds to address whatif questions on capacity planning. From textbook: pages 114122 
October 19, 2018  Review of performance bounds, their interpretation for open networks. From textbook: ex 7.2 (acd), 7.3, 6.3, 6.4 
October 24, 2018  Performance bounds and timeline analysis with example. From textbook: ex 7.2 (b), 7.4, 7.5 
October 26, 2018  Stochastic processes, discrete and continuous. Discrete Time Markov Chains (DTMC): Markovian property, time homogeneity. 1step transition probability matrix. ChapmanKolmogoroff equations. nstep transition probability matrix. Limiting probability and limiting distribution of a DTMC. From textbook: pages 127135. 
October 31, 2018  Review of stochastic processes, DTMCs, transition probability matrix in one and multiple steps, limiting probabilities. Stationary equations. Infinite state DTMCs. 
November 2, 2018  Lesson cancelled 
November 7, 2018  Midterm 
November 9, 2018  Infinite state DTMCs and related stationary equations. Examples of DTMC analysis: one server with infinite queue. From textbook: pages 142145 From textbook: ex 8.1, 8.2, 8.3, 8.6 
November 14, 2018  Ergodicity theory. Ergodicity in finitestate DTMC (existence of the limiting distribution). Conditions for existence of the limiting distributions in finitestate DTMC. Definition of period in a finitestate DTMC. Aperiodicity. Irreducibility. Relationship between time recurrence and irreducibility in finitestate DTMCs. Stationary equations and flow balance equations. Ergodicity in infinite state DTMCs. Examples of positive recurrent, transient and nullrecurrent DTMCs. Limiting probabilities interpreted as rates, flow balance and stationary equations. From textbook: pages 148160, 164166, 168171 + ex 9.10 
November 16, 2018  A discussion on limiting and stationary distributions. Realworld examples: Google PageRank algorithm. Poissonian processes and exponential distribution  an indepth discussion on definitions and properties. Additivity of Poissonian processes. A preliminary study of a single server system with Poissonian arrivals and Exponential service times. From textbook: pages 190195, 206  207 + 213  216 
November 21, 2018  Continuous Time Markov Chains (CTMC). Uniform time observation of nonuniform processes. Uniformization and discretization. Embedded Discrete Time Markov Chain of a nonuniform continuous time process. Study of the M/M/1/inf queue: flow balance equations, utilization, population, throughput, response time, queue population, average waiting time. Process with a server without queue: throughput, loss rate, utilisation, average population, average response time. Finite queue servers. From textbook: pages 225  226, 229  234, 236  239 + ex 13.1, 13.2, 13.4 + assignment 13.5 
November 23, 2018  Continuous time Markov processes representing systems with multiple classes and admission control. Thresholdbased and hysteresis policies. Capacity planning for performance requirements. Exercise from previous year exams. 
November 28, 2018  Capacity planning in single server (Bertsekas Gallager result, and buffer sizing). Capacity planning of a cluster of m servers each with its own queue, how to determine the number of servers in a cluster to meet performance constraints (response time, waiting time, queue length, theoretical limitations). Server farms: kserver loss systems, M/M/k queueing systems with finite and infinite queue Utilization in a multiple server system. From textbook: pages 253264 + several exercizes taken from other books. Assignment: ex 14.3, 14.5, 14.6. 
November 30, 2018  Boolean Network Tomography: identifiability and kidentifiability, projects Slides on tomography available here: Link 1 Link 2 
December 5, 2018  Drone trajectory planning, projects. Slides on centralized task assignment for a network of aerial drones: Link 1 
December 7, 2018  Practice with finite state chains: exact and asymptotic analysis. Closed networks with routing cycles in the subsystem, tandem servers with finite buffer size, closed networks with multiple devices. Comparison of a system with a unique fast server and one with m servers m times slower (statistical and frequency division multiplexing). From textbook: pages 239242, 282285 + 16.1, 16.2. 
December 12, 2018  Jackson networks, Jackson theorem (with proof), product form solution for the limiting probabilities, average number of jobs in a Jackson network. From textbook: pages 297306 + 17.1. 
December 14, 2018  Discussion on Jackson theorem and related assumptions on arrivals, alternative ways to solve networks with feedback loops. From textbook: 17.1 (discussion), 17.2, 17.3, 17.4. 
December 19, 2018  Networks of multiple devices, which do not have product form solution and why, examples. Exercizes from previous exams. From textbook: 18.6, 18.1, 18.2 (suggested to read chapter 18). 
December 21, 2018  Lesson moved to the afternoon Midterm 
Mor HarcolBalter, Performance Modeling and Design of Computer Systems, Cambridge University Press, 2013.
I  Attachment  History  Action  Size  Date  Who  Comment 

CNP_projects.pdf  r1  manage  302.7 K  20190102  18:06  NovellaBartolini  
TesiProgettiPerfCompNet_Part1.pdf  r1  manage  8516.4 K  20190102  13:00  NovellaBartolini  
TesiProgettiPerfCompNet_Part2.pdf  r1  manage  8516.6 K  20190102  13:00  NovellaBartolini 
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