##
###
Event Relationship Graph Lite: Event based modeling for simulation-optimization of control policies in discrete event systems

Andrea Matta, Giulia Pedrielli, Arianna Alfieri

2014
*
Proceedings of the Winter Simulation Conference 2014
*

Simulation-optimization has received a spectacular attention in the past decade. However, the theory still cannot meet the requirements from practice. Decision makers ask for methods solving a variety of problems with diverse aggregations and objectives. To answer these needs, the interchange of solution procedures becomes a key requirement as well as the development of (1) general modeling methodologies able to represent, extend and modify simulation-optimization as a unique problem, (2)
## more »

... problem, (2) mapping procedures between formalisms to enable the use of different tools. However, no formalism treats simulation-optimization as an integrated problem. This work aims at partially filling this gap by proposing a formalism based upon Event Relationship Graphs (ERGs) to represent the system dynamics, the problem decision variables and the constraints. The formalism can be adopted for simulation-optimization of control policies governing a queueing network. The optimization of a Kanban Control System is proposed to show the whole approach and its potential benefits. 3983 978-1-4799-7486-3/14/$31.00 ©2014 IEEE Matta, Pedrielli, and Alfieri Concerning the modeling methodologies, most of the research was devoted to develop simulation or optimization rather than simulation-optimization formalisms. Schruben (1983) proposed the Event Relationship Graph (ERG), a general language for modeling and simulation of discrete event systems (DESs). ERGs have been demonstrated to be able to simulate a Turing machine and have been successfully applied to the evaluation of the performance of DESs. Moreover, ERG solving optimization problems were proposed (Savage et al. 2005 , Chan 2005 ). In Liu et al. (2012) , an ERG is automatically generated from real time data to first simulate and then optimize the system. The LEGO framework was proposed to develop simulation model components using ERGs (Buss and Sanchez 2002) . In the computing area, several modeling techniques are used for simulation and property verification, but few have the ERG modeling power and generality. An ERG can model a petri net but not vice versa. The well known GSMP (Generalized Semi-Markov Process) and DEVS (Discrete Event System Specification (Zeigler 1976)) formalisms have the same modeling power of ERG (Savage, Schruben, and Yücesan 2005) but they are not easy to use in many practical applications. State based formalisms (e.g., finite state automata) manifest their drawbacks when complex systems composed of several components are modeled due to the state space growth, which is typically faster than the increase in the number of events (Cassandras and Lafortune 2008, Cao and Zhang 2008) . Also DEVS and GSMP (Iglehart and Shedler 1983), despite their generality, suffer from the state space growth problem. Concerning the mapping procedures, Chan and Schruben (2008) proved a general scheme to translate ERG models into their mathematical programming counterpart. However, this was done in the scope of simulation. The translation into mathematical programming was then extended to simulation-optimization of multi-stage tandem queueing systems in Matta (2008), Alfieri and Matta (2012). Recently, Latorre and Jiménez (2013) proposed a tree-based petri net model (modeling formalism) to solve a resource allocation problem. This paper explores the possibility of developing an event-based modeling language for DES simulationoptimization problems using ERGs. More specifically, a restricted class of ERGs (namely Event Relationship Graph Lite, ERGL or ERG Lite) is used to simultaneously represent the dynamics of the DES together with the constraints and the decision variables of the optimization problem. This integrated ERG contains most of the information (the objective function can be implicitly included only in particular cases) needed to estimate the performance and to solve the optimization problem(s) related to the DES underlying the developed graph. This preliminary study deals with a subclass of ERGs. Because of this restriction, the class of optimization problems under investigation is confined to the selection of the optimal control policy for multi-stage queueing systems. Despite the current limitations of ERGLs in terms of expressiveness of the formalism, the class of DESs and the problems they can model is vast and relevant in practice (e.g., buffer allocation problems, maintenance policies, production control policies, etc.). The contribution of this work is twofold. The proposed simplified ERG is proven to be capable of representing the useful information for solving the simulation-optimization problems of a controlled DES. Either a simulation or a simulation-optimization model with different levels of approximation are generated using mathematical programming. A second contribution is the clear distinction between system modeling and control modeling. This paper formally defines the system object of the simulation-optimization as a controlled ERGL, i.e., the union of a natural model (the DES without any control) and the control model (the control mechanism added to govern the DES). The decomposability is only possible thanks to the use of a unique formalism able to handle both structural and control information. GENERAL NOTATION The topology of the DES we consider can be represented by a queueing network with the set of servers J = {0, . . . , J + 1} and the set of possible transaction routes for job i (i ∈ N = {0, .

doi:10.1109/wsc.2014.7020223
dblp:conf/wsc/MattaPA14
fatcat:jcgwd6eic5d6lf6ftj656r3hiq