Variability in a single compartment system: A note on S. R. Bernard's model

In this note we examine a continuous time version of a compartmental model introduced in a discrete time setting by S. R. Bernard. The model allows for more than one particle to leave the system at any time. This introduces additional randomness into the system, over the pure death system and this is reflected in the variance function.     

Stochastic theory of compartments: One and two compartment systems

Previous work on compartmental systems is generalized (i) to allow the particles present at time zero to have a different lifetime distribution than those which arrive after time zero, and (ii) to allow a particle which enters the system at timet to have a lifetime distribution which is a function oft but is otherwise quite general. The one and two compartment models are analyzed under the above conditions and compared to previous results of Thakuret al. (1974), Purdue (1974) and Cardenas and Matis (1974). Finally, some results for the two compartment, reversible system are given. The analysis used is a blend of direct random variable and queueing theoretic techniques.     

Stochastic theory of compartments: An open,two compartment,reversible system with independent poisson arrivals

This paper discusses two compartment models with interaction allowed between the compartments. The total number of particles in the system at any time is discussed along with the number to the found in each separate compartment. An interesting result is that the number of particles in each of the two compartments areindependent random variables. Some asymptotic results are also given. The paper is a continuation of some earlier work by the author.