Discrete Time Hybrid Semi-Markov Models in Manpower Planning

Discrete time Markov models are used in a wide variety of social sciences. However, these models possess the memoryless property, which makes them less suitable for certain applications. Semi-Markov models allow for more flexible sojourn time distributions, which can accommodate for duration of stay effects. An overview of differences and possible obstacles regarding the use of Markov and semi-Markov models in manpower planning was first given by Valliant and Milkovich (1977). We further elaborate on their insights and introduce hybrid semi-Markov models for open systems with transition-dependent sojourn time distributions. Hybrid semi-Markov models aim to reduce model complexity in terms of the number of parameters to be estimated by only taking into account duration of stay effects for those transitions for which it is useful. Prediction equations for the stock vector are derived and discussed. Furthermore, the insights are illustrated and discussed based on a real world personnel dataset. The hybrid semi-Markov model is compared with the Markov and the semi-Markov models by diverse model selection criteria.

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Sojourn times in finite Markov processes

Journal of Applied Probability ◽

10.2307/3214379 ◽

1989 ◽

Vol 26 (4) ◽

pp. 744-756 ◽

Cited By ~ 75

Author(s):

Gerardo Rubino ◽

Bruno Sericola

Keyword(s):

Markov Process ◽

Asymptotic Behaviour ◽

Markov Processes ◽

Discrete Time ◽

Continuous Time ◽

Sojourn Time ◽

Sojourn Times ◽

Finite State ◽

Sojourn Time Distributions ◽

Finite State Space

Sojourn times of Markov processes in subsets of the finite state space are considered. We give a closed form of the distribution of the nth sojourn time in a given subset of states. The asymptotic behaviour of this distribution when time goes to infinity is analyzed, in the discrete time and the continuous-time cases. We consider the usually pseudo-aggregated Markov process canonically constructed from the previous one by collapsing the states of each subset of a given partition. The relation between limits of moments of the sojourn time distributions in the original Markov process and the moments of the corresponding holding times of the pseudo-aggregated one is also studied.

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Comparison of Sojourn Time Distributions in Modeling HIV/AIDS Disease Progression

Biometrical Letters ◽

10.1515/bile-2017-0009 ◽

2017 ◽

Vol 54 (2) ◽

pp. 155-174 ◽

Cited By ~ 1

Author(s):

Tilahun Ferede Asena ◽

Ayele Taye Goshu

Keyword(s):

Weibull Distribution ◽

Disease Progression ◽

Sojourn Time ◽

Markov Models ◽

Transition Probability ◽

Good State ◽

Rate Of Decline ◽

Sojourn Time Distributions ◽

Over Time ◽

Hiv Aids

Summary An application of semi-Markov models to AIDS disease progression was utilized to find best sojourn time distributions. We obtained data on 370 HIV/AIDS patients who were under follow-up from September 2008 to August 2015, from Yirgalim General Hospital, Ethiopia. The study reveals that within the “good” states, the transition probability of moving from a given state to the next worst state has a parabolic pattern that increases with time until it reaches a maximum and then declines over time. Compared with the case of exponential distribution, the conditional probability of remaining in a good state before moving to the next good state grows faster at the beginning, peaks, and then declines faster for a long period. The probability of remaining in the same good disease state declines over time, though maintaining higher values for healthier states. Moreover, the Weibull distribution under the semi-Markov model leads to dynamic probabilities with a higher rate of decline and smaller deviations. In this study, we found that the Weibull distribution is flexible in modeling and preferable for use as a waiting time distribution for monitoring HIV/AIDS disease progression.

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