Computing Average Response Time

Responsiveness—the requirement that every request to a system be eventually handled—is one of the fundamental liveness properties of a reactive system. Average response time is a quantitative measure for the responsiveness requirement used commonly in performance evaluation. We show how average response time can be computed on state-transition graphs, on Markov chains, and on game graphs. In all three cases, we give polynomial-time algorithms.

[1]  L. Brim,et al.  Faster algorithms for mean-payoff games , 2011, Formal Methods Syst. Des..

[2]  Krishnendu Chatterjee,et al.  Nested Weighted Limit-Average Automata of Bounded Width , 2016, MFCS.

[3]  Krishnendu Chatterjee,et al.  Quantitative Automata under Probabilistic Semantics , 2016, 2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS).

[4]  Krishnendu Chatterjee,et al.  Quantitative languages , 2008, TOCL.

[5]  J. Filar,et al.  Competitive Markov Decision Processes , 1996 .

[6]  Uri Zwick,et al.  The Complexity of Mean Payoff Games on Graphs , 1996, Theor. Comput. Sci..

[7]  Krishnendu Chatterjee,et al.  Nested Weighted Automata , 2015, 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science.

[8]  Richard M. Karp,et al.  A characterization of the minimum cycle mean in a digraph , 1978, Discret. Math..

[9]  Krishnendu Chatterjee,et al.  Efficient and Dynamic Algorithms for Alternating Büchi Games and Maximal End-Component Decomposition , 2014, J. ACM.

[10]  A. Ehrenfeucht,et al.  Positional strategies for mean payoff games , 1979 .

[11]  M. Droste,et al.  Handbook of Weighted Automata , 2009 .

[12]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[13]  Krishnendu Chatterjee,et al.  Bidirectional Nested Weighted Automata , 2017, CONCUR.

[14]  Krishnendu Chatterjee,et al.  An O(n2) time algorithm for alternating Büchi games , 2011, SODA.

[15]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .