The objective of the course is to introduce analytical tools that are needed to construct/measure/analyze
models of resource contention systems, e.g. computer systems, networks. This course enables one
to answer questions such as:
• what is the throughput of the wifi 802.11 protocol?
• if both the arrival and the service rates double, will the response time stay the same?
• given the choice between a single machine with speed s, or n machines each with speed s/n, which should one choose?
• how many operators in a call center are needed to keep the rejection probability of incoming requests low?
Given a system (Internet, department WLAN, web server, . . .), we could be interested to know
how well it performs, we could need to adjust its design or to change its scale. Appropriate per-
formance metrics are the average response time, the quality of service (user’s point of view), the
throughput or the number of supported sessions (system’s point of view). Other metrics are related
to the utilization of the system, its reliability, or its availability.
The course will cover Markov chains in 3 lectures and queueing theory in 3 lectures. The last session is devoted to few use case applications.