Tag Archives: Stochastic Models

15/11/2016 – Talk by Andrea Marin

Title: Fair workload distribution for multi-server systems with pulling strategies
Time: 13:00
Location: Meeting room, Building Zeta
Type: Research Result
Speaker: Andrea Marin
Abstract:
In this talk we present the paper that has received the best paper award at the conference Valuetools 2016.

We consider systems with a single queue and multiple parallel servers. Each server fetches a job from the queue immediately after completing its current work. We propose a pulling strategy that aims at achieving a fair distribution of the number of processed jobs among the servers. We show that if the service times are exponentially distributed then our strategy ensures that in the long run the expected difference among the processed jobs at each server is finite while maintaining a reasonable throughput.
We give the analytical expressions for the stationary distribution and the relevant stationary performance indices like the throughput and the system’s balance.
Interestingly, the proposed strategy can be used to control the join-queue length in fork-join queues and the analytical model gives the closed form expression of the performance indices in saturation.

02/03/2016 – Talk by Filippo Cavallin

Title:  Cronization: a method to pass from Continuous Time to Discrete Time Automata
Time: 14:00
Location: Meeting room, building Zeta
Type: Research Result
Speaker: Filippo Cavallin
Abstract:
Discrete and Continuous Time automata are important formalisms to model and analyze systems such queuing and telecommunication networks. The stationary performance analysis of these automata requires the computation of the steady-state distribution of their underlying Markov chains. Sometimes for the analysis is more convenient to pass from continuous to discrete time. The main methods are focused on the underlying Markov chains and not on the automatas. To preserve the transitions with labels and the synchronization between them, we will introduce a method to pass from a continuous time stochastic automaton (SA) to a probabilistic Input/Output automaton (PIOA). This method is a bijection from continuous to discrete time and it allows us to switch between the two different types of automata and it preserves the parallel composition.

04/03/2015 Talk by Filippo Cavallin

Title: Single TTL Cache with Reset under the Independent Reference Model
Time: 14:00
Location: Conference room, Building Alfa
Type: Research Result
Speaker: Filippo Cavallin
Abstract:
Cache systems based on a Time To Live (TTL) policy are becoming increasingly important especially in the field of Information-Centric Network design. In this kind of cache an element is kept in it unless it is not used (i.e., it does not receive any write/read request) for a certain period.
This model is less effective if there are some periods of inactivity of the system.
In this talk, after some brief explanations about G-Networks and PEPA language, we will evaluate the performance of a single TTL cache equipped with a refresh system that rejuvenates the timers of the elements stored. In this way we try to avoid the problem of under-utilization of the cache when traffic is low. We will show also that the equilibrium distribution function has a product-form expression under the Independent Reference Model. This allows us to efficiently compute the performance indices.