Sergei M. Ermakov, Nikolai K. Krivulin
Serial and parallel algorithms for simulation of tandem queueing systems with infinite buffers are presented, and their performance is examined. It is shown that the algorithms which are based on a simple computational procedure involve low time and memory requirements.
Nikolai K. Krivulin
A class of queueing networks which consist of single-server fork-join nodes with infinite buffers is examined to derive a representation of the network dynamics in terms of max-plus algebra. For the networks, we present a common dynamic state equation which relates the departure epochs of customers from the network nodes in an explicit vector form determined by a state transition matrix. We show how the matrix may be calculated from the service time of customers in the general case, and give examples of matrices inherent in particular networks.
Nikolai K. Krivulin
A class of queueing networks which may have an arbitrary topology, and consist of single-server fork-join nodes with both infinite and finite buffers is examined to derive a representation of the network dynamics in terms of max-plus algebra. For the networks, we present a common dynamic state equation which relates the departure epochs of customers from the network nodes in an explicit vector form determined by a state transition matrix. It is shown how the matrices inherent in particular networks may be calculated from the service times of customers. Since, in general, an explicit dynamic equation may not exist for a network, related existence conditions are established in terms of the network topology.
Nikolai K. Krivulin
Simple lower and upper bounds on mean cycle time in stochastic acyclic fork-join queueing networks are derived using a (max,+)-algebra based representation of network dynamics. The behaviour of the bounds under various assumptions concerning the service times in the networks is discussed, and related numerical examples are presented.
Nikolai K. Krivulin
An overview of the recursive equations based models and their applications in simulation based analysis and optimization of queueing systems is given. These models provide a variety of systems with a convenient and unified representation in terms of recursions for arrival and departure times of customers, which involves only the operations of maximum, minimum, and addition.
Nikolai K. Krivulin
Simple lower and upper bounds on mean cycle time in stochastic acyclic fork-join networks are derived using the $(\max,+)$-algebra approach. The behaviour of the bounds under various assumptions concerning the service times in the networks is discussed, and related numerical examples are presented.
Nikolai K. Krivulin
A stochastic dynamical system represented through a linear vector equation in idempotent algebra is considered. We propose simple bounds on the mean growth rate of the system state vector, and give an analysis of absolute error of a bound. As an illustration, numerical results of evaluation of the bounds for a test system are also presented.
Sergei M. Ermakov, Nikolai K. Krivulin
Parallel algorithms designed for simulation and performance evaluation of single-server tandem queueing systems with both infinite and finite buffers are presented. The algorithms exploit a simple computational procedure based on recursive equations as a representation of system dynamics. A brief analysis of the performance of the algorithms are given to show that they involve low time and memory requirements.