Stationary distributions of open Markov processes in discrete time with application to hospital planning

Abstract

Suppose that a new hospital is to be planned or an existing one reorganized according to the modern Progressive Patient Care System (Hartley et al. (1968)). In this system, there are three types of wards, viz.

On the distribution of attributes in organizations

“…In this field many papers have been published taking into consideration special structure properties of hospitals (cf. Bithell (1971), Staff and Vagholkar (1971)).…”

Open Markov Chains: Cumulant Dynamics, Fluctuations and Correlations

“…Guerreiro and colleges have also studied a class of open of population models subjected to periodical re-classifications [ 12 , 13 , 14 ]. The case of open Markov chains with Poisson recruitment has been dealt in [ 15 ], and remarkable extensions of these models to continuous time has been studied in [ 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 ]. Open Markov chain schemes fed by a second order stationary and non-stationary processes have also been studied in [ 24 ] where the authors consider that the inflow of new population elements is modeled by a time series coming from a second order stationary process, i.e., a stationary process with a deterministic bias.…”

“…All these different models of stochastic open systems have been useful for several important applications. These models have been used to study consumption credit portfolios [ 26 ], open automobile portfolios [ 27 , 28 ], hospital planning [ 19 ], enrollments and degrees awarded in universities [ 8 ], manpower models [ 20 , 21 , 29 ] as well as traffic flow by means of random networks [ 30 ]. Open Markov processes have also been used to understand in general several properties of bonus-malus systems [ 9 , 10 , 11 , 27 ].…”

Stationarity of a stochastic population flow model

“…In the special case where (X (t )) t ∈N is a sequence of independent and identically distributed random vectors, Y (t ) is a homogeneous Markov chain (MC). For MCs of this kind [4] gives some explicit results mainly for geometrically distributed input; for Poisson input see [3]. The known results in this case are expounded in [1].…”