Journal:Informatica
Volume 5, Issues 1-2 (1994), pp. 211–230
Abstract
The paper deals with a simple model of the competition of two queuing systems, providing the same service. Each system may vary its service price and its service rate. The customers choose the system with less total service price, that depends on the waiting time and on the service price. The possibility for the existence of equilibrium is investigated. Simple cases are investigated analytically. It is shown that the Nash equilibrium exists in special cases only. A modification of the Stakelberg equilibrium is proposed as a model of competition with a prognosis. This prognosis helps form more stable prices and more stable strategies of competitors. The case of social economics is investigated, too. The dynamics of the competition of more realistic stochastic queuing systems is investigated by Monte Carlo simulation. The simulative analysis is realized by means of a rule-based simulation system.
Journal:Informatica
Volume 5, Issues 1-2 (1994), pp. 167–174
Abstract
We consider here the optimization problems of simple competitive model. There are two servers providing the some service. Each server fix the price and the rate of service. The rate of service defines the customer losses waiting in line for the service. The customer go to the server with lesser total service cost. The total cost includes the service price plus waiting losses. A customer goes away, if the total cost exceeds some critical level. The flow of customers and the service time both are stochastic. There is no known analytical solution for this model. We get the results by Monte Carlo simulation. We get the analytical solution of the simplyfied model.
We use the model as an illustration to show the possibilities and limitations of optimization theory and numerical techniques in the competitive models.
We consider optimization in two different mathematical frameworks: the fixed point and the Lagrange multipliers. We consider two different economic and social objectives, too: the equilibrium and the social cost minimization.
We use the model teaching Operations Research. The simple model may help to design more realistic models describing the processes of competition.