Modelling and analysis of Markovian continuous flow systems with a finite buffer

Abstract

In this study, a Markovian fluid flow system with two stages separated by a finite buffer is considered. Fluid flow models have been analyzed extensively to evaluate the performance of production, computer, and telecommunication systems. Recently, we developed a methodology to analyze general Markovian continuous flow systems with a finite buffer. The flexibility of this methodology allows us to analyze a wide range of systems by specifying the transition rates and the flow rates associated with each state of each stage. In this study, in order to demonstrate the applicability of our methodology, we model and analyze a range of models studied in the literature. The examples we analyze as special cases of our general model include systems with phase-type failure and repair-time distributions, systems with machines that have multiple up and down states, and systems with multiple unreliable machines in series or parallel in each stage. For each case, the Markovian model is developed, the transition and flow rates are determined, and representative numerical results are obtained by using our methodology.

Production Systems Flow Modelling Using Decomposition Method and Required Buffers

“…A stochastic process is a random variable indexed by a parameter; we denote it by X(t). A Markov chain is a stochastic process where the domain of the variable is a countable set and the following relation is satisfied: [12].…”

“…Usually, we will apply the following states: idle, busy, blocked. For the state x i , we define the outgoing rate as the sum of all transition rates from x i to all x j 's where i  j [12,13].…”

Simulating Continuous Time Production Flows in Food Industry by Means of Discrete Event Simulation

“…Typically, mathematical modeling is used to model the system and to obtain the closed-form solutions. The base unit model is the so-called twomachine one-buffer building block, whose first models were proposed by Zimmern [13], Gershwin and Schick [14], Yeralan and Tan [15], and that obtained several improvements in years to enhance its capability to represent the behavior of real systems [16][17][18][19][20]. This building block is able to represent a simple series of two machines (a simple line) in which the decoupling effect of a buffer is also considered, and then it is the minimal requirement need to model a flow-based manufacturing system.…”

Optimal maintenance of a series production system with two multi-component subsystems and an intermediate buffer

“…Tan and Gershwin [20] investigated the steady-state of a general Markovian two-stage continuous-flow system by solving a system of differential equations that describes the dynamics of the system. After that, Tan and Gershwin [19] further applied their model to the steadystate analysis of more general situations, e.g. systems with multiple components in series or parallel in each subsystem.…”