Multiple Class G-Networks with Restart Jean-Michel Fourneau, Katinka - PowerPoint PPT Presentation

Multiple Class G-Networks with Restart Jean-Michel Fourneau, Katinka Wolter , Philipp Reinecke, Tilman Krauß and Alexandra Danilkina PRiSM, CNRS Freie Universit¨ at Berlin HP Labs Bristol Universit´ e de Versailles Institut f¨ ur Informatik Long Down Avenue, France Bristol, UK ISCAS, 26 September 2013

Table of Contents 1 The restart method 2 Evaluation Approaches 3 The model 4 Examples 5 Conclusions 1 / 11

The restart method request ://www Restart: A client sends a request. 2 / 11

The restart method Restart: A client sends a request. If there is no response within a reasonable time, 2 / 11

The restart method restart request ://www Restart: A client sends a request. If there is no response within a reasonable time, the request is repeated 2 / 11

The restart method response Restart: A client sends a request. If there is no response within a reasonable time, the request is repeated 2 / 11

The restart method response Restart: A client sends a request. If there is no response within a reasonable time, the request is repeated Restart may reduce response-times 2 / 11

The restart method ://www request request ://www request ://www Restart: A client sends a request. If there is no response within a reasonable time, the request is repeated Restart may reduce response-times Many clients send a request. 2 / 11

The restart method Restart: A client sends a request. If there is no response within a reasonable time, the request is repeated Restart may reduce response-times Many clients send a request. If there is no response within a reasonable time, 2 / 11

The restart method ://www repeat request repeat request ://www repeat request ://www Restart: A client sends a request. If there is no response within a reasonable time, the request is repeated Restart may reduce response-times Many clients send a request. If there is no response within a reasonable time, the request is repeated 2 / 11

The restart method response response response Restart: A client sends a request. If there is no response within a reasonable time, the request is repeated Restart may reduce response-times Many clients send a request. If there is no response within a reasonable time, the request is repeated Question: Will restart reduce response-times for all? 2 / 11

The restart method response response response Restart: A client sends a request. If there is no response within a reasonable time, the request is repeated Restart may reduce response-times Many clients send a request. If there is no response within a reasonable time, the request is repeated Question: Will restart reduce response-times for all? Insight useful for 2 / 11

The restart method response response response Restart: A client sends a request. If there is no response within a reasonable time, the request is repeated Restart may reduce response-times Many clients send a request. If there is no response within a reasonable time, the request is repeated Question: Will restart reduce response-times for all? Insight useful for Optimising software performance 2 / 11

The restart method response response response Restart: A client sends a request. If there is no response within a reasonable time, the request is repeated Restart may reduce response-times Many clients send a request. If there is no response within a reasonable time, the request is repeated Question: Will restart reduce response-times for all? Insight useful for Optimising software performance Development of benchmarks 2 / 11

Evaluation Approaches Experimentation on test-beds – low abstraction level Set up the system in the lab Cost and time constraints Results do not generalise 3 / 11

Evaluation Approaches Experimentation on test-beds – low abstraction level Set up the system in the lab Cost and time constraints Results do not generalise Simulations – medium abstraction level Build a simulation (e.g. NS-2, OMNeT++, M¨ obius) Give slightly more general results than measurement studies Results are less realistic 3 / 11

Evaluation Approaches � x F ( x ) = 0 f ( u ) du Experimentation on test-beds – low abstraction level Set up the system in the lab Cost and time constraints Results do not generalise Simulations – medium abstraction level Build a simulation (e.g. NS-2, OMNeT++, M¨ obius) Give slightly more general results than measurement studies Results are less realistic Analytical Approaches – high abstraction level Formalise problem Give general insights Results might be far from reality 3 / 11

G-networks one could guess, a G-network is a genetic network 4 / 11

G-networks one could guess, a G-network is a genetic network it is not. 4 / 11

G-networks one could guess, a G-network is a genetic network it is not. G as generalized queueing network or Gelenbe network 4 / 11

G-networks one could guess, a G-network is a genetic network it is not. G as generalized queueing network or Gelenbe network A G-network is an open queueing network with several types of customers regular jobs negative customers, signals (signals between queues) 4 / 11

G-networks Class 1 Class changes upon restart Class 2 Jobs PS Restart Signals Class K Jobs arrive into one of K classes 5 / 11

G-networks Class changes Class 1 upon restart Class 2 Jobs PS Restart Signals Class K Jobs arrive into one of K classes Service time PH-distributed 5 / 11

G-networks Class changes Class 1 upon restart Class 2 Jobs PS Restart Signals Class K Jobs arrive into one of K classes Service time PH-distributed One class of signals (restarts) with success probability 5 / 11

G-networks Class changes Class 1 upon restart Class 2 Jobs PS Restart Signals Class K Jobs arrive into one of K classes Service time PH-distributed One class of signals (restarts) with success probability Upon restart a job changes class, routing probability, success probabilities 5 / 11

G-networks Class 1 Class changes upon restart Class 2 Jobs PS Restart Signals Class K Jobs arrive into one of K classes Service time PH-distributed One class of signals (restarts) with success probability Upon restart a job changes class, routing probability, success probabilities Markovian model 5 / 11

G-networks Class changes Class 1 Queue i Queue j upon restart Class 1 Class 1 Class changes upon restart Class 2 Jobs Class 2 Class 2 Jobs Jobs PS PS PS Restart Signals Class K Restart Signals Class K Class K Restart Signals Jobs arrive into one of K classes Service time PH-distributed One class of signals (restarts) with success probability Upon restart a job changes class, routing probability, success probabilities Markovian model Product-form solution 5 / 11

G-networks Class changes Class 1 Queue i Queue j upon restart Class 1 Class 1 Class changes upon restart Class 2 Jobs Class 2 Class 2 Jobs Jobs PS PS PS Restart Signals Class K Restart Signals Class K Class K Restart Signals Jobs arrive into one of K classes Service time PH-distributed One class of signals (restarts) with success probability Upon restart a job changes class, routing probability, success probabilities Markovian model Product-form solution Derivation of standard queueing metrics straight forward 5 / 11

First example: iid services Model represents infinite restarts 6 / 11

First example: iid services Model represents infinite restarts Jobs arrive to class 1 at rate 0 . 012 6 / 11

First example: iid services Exp(2) 0.9 Exp(5) 0.1 Exp(0.1) Model represents infinite restarts Jobs arrive to class 1 at rate 0 . 012 PH-distributed service time, scv = 6 . 7539 6 / 11

First example: iid services Model represents infinite restarts Jobs arrive to class 1 at rate 0 . 012 PH-distributed service time, scv = 6 . 7539 Determine utilisation, expected queue length and expected waiting time 6 / 11

Second example: 5 classes Class changes Class 1 upon restart Class 2 Jobs PS Restart Signals Class 5 Jobs arrive only to class 1 at rate 0 . 1 7 / 11

Second example: 5 classes Class changes Class 1 upon restart class 1 Exp(1) Exp(1) Class 2 Jobs class 2 Exp(2) Exp(2) PS class 3 Exp(3) Exp(3) class 4 Exp(4) Exp(4) class 5 Exp(5) Exp(5) Restart Signals Class 5 Jobs arrive only to class 1 at rate 0 . 1 Successively faster Erlang(2) service, i.e. µ ( k,p ) = (1 , 2 , 3 , 4 , 5) 7 / 11

Second example: 5 classes Class changes Class 1 upon restart class 1 Exp(1) Exp(1) Class 2 Jobs class 2 Exp(2) Exp(2) PS class 3 Exp(3) Exp(3) class 4 Exp(4) Exp(4) class 5 Exp(5) Exp(5) Restart Signals Class 5 Jobs arrive only to class 1 at rate 0 . 1 Successively faster Erlang(2) service, i.e. µ ( k,p ) = (1 , 2 , 3 , 4 , 5) Restart with resume semantics - work is not lost 7 / 11

Second example: 5 classes Class changes Class 1 upon restart Class 2 Jobs PS Restart Signals Class 5 Jobs arrive only to class 1 at rate 0 . 1 Successively faster Erlang(2) service, i.e. µ ( k,p ) = (1 , 2 , 3 , 4 , 5) Restart with resume semantics - work is not lost Completed jobs leave with prob 1. 7 / 11