Reward processes with nonlinear reward functions

1996 ◽  
Vol 33 (4) ◽  
pp. 1011-1017 ◽  
Author(s):  
A. Reza Soltani
Keyword(s):  
Markov Process ◽  
Explicit Formula ◽  
Sojourn Time ◽  
Time Distribution ◽  
Reward Function ◽  
Sojourn Time Distribution ◽  
Semi Markov Process ◽  
Reward Process ◽  
Reward Functions

Based on a semi-Markov process J(t), t ≧ 0, a reward process Z(t), t ≧ 0, is introduced where it is assumed that the reward function, p(k, x) is nonlinear; if the reward function is linear, i.e. ρ (k, x) = kx, the reward process Z(t), t ≧ 0, becomes the classical one, which has been considered by many authors. An explicit formula for E(Z(t)) is given in terms of the moments of the sojourn time distribution at t, when the reward function is a polynomial.

Reward processes with nonlinear reward functions

1996 ◽  
Vol 33 (04) ◽  
pp. 1011-1017 ◽  
Author(s):  
A. Reza Soltani
Keyword(s):  
Markov Process ◽  
Explicit Formula ◽  
Sojourn Time ◽  
Time Distribution ◽  
Reward Function ◽  
Sojourn Time Distribution ◽  
Semi Markov Process ◽  
Reward Process ◽  
Reward Functions

Based on a semi-Markov process J(t), t ≧ 0, a reward process Z(t), t ≧ 0, is introduced where it is assumed that the reward function, p(k, x) is nonlinear; if the reward function is linear, i.e. ρ (k, x) = kx, the reward process Z(t), t ≧ 0, becomes the classical one, which has been considered by many authors. An explicit formula for E(Z(t)) is given in terms of the moments of the sojourn time distribution at t, when the reward function is a polynomial.

scholarly journals The sojourn time distribution in an infinite server resequencing queue with dependent interarrival and service times

2002 ◽  
Vol 39 (03) ◽  
pp. 590-603 ◽  
Author(s):  
Tijs Huisman ◽  
Richard J. Boucherie
Keyword(s):  
Markov Process ◽  
General Model ◽  
Sojourn Time ◽  
Time Distribution ◽  
Arrival Process ◽  
Accurate Approximation ◽  
Infinite Server ◽  
Sojourn Time Distribution ◽  
Semi Markov Process ◽  
Service Times

We consider an infinite server resequencing queue, where arrivals are generated by jumps of a semi-Markov process and service times depend on the jumps of this process. The stationary distribution of the sojourn time, conditioned on the state of the semi-Markov process, is obtained both for the case of hyperexponential service times and for the case of a Markovian arrival process. For the general model, an accurate approximation is derived based on a discretisation of interarrival and service times.

scholarly journals The sojourn time distribution in an infinite server resequencing queue with dependent interarrival and service times

2002 ◽  
Vol 39 (3) ◽  
pp. 590-603 ◽  
Author(s):  
Tijs Huisman ◽  
Richard J. Boucherie
Keyword(s):  
Markov Process ◽  
General Model ◽  
Sojourn Time ◽  
Time Distribution ◽  
Arrival Process ◽  
Accurate Approximation ◽  
Infinite Server ◽  
Sojourn Time Distribution ◽  
Semi Markov Process ◽  
Service Times

We consider an infinite server resequencing queue, where arrivals are generated by jumps of a semi-Markov process and service times depend on the jumps of this process. The stationary distribution of the sojourn time, conditioned on the state of the semi-Markov process, is obtained both for the case of hyperexponential service times and for the case of a Markovian arrival process. For the general model, an accurate approximation is derived based on a discretisation of interarrival and service times.

An invariance principle for semi-Markov processes

1985 ◽  
Vol 17 (1) ◽  
pp. 100-126
Author(s):  
D. McDonald
Keyword(s):  
Sojourn Time ◽  
Time Distribution ◽  
Invariant Probability Measure ◽  
Transition Kernel ◽  
Mixing Conditions ◽  
Sojourn Time Distribution ◽  
Semi Markov Process ◽  
Image Position ◽  
Expected Sojourn Time ◽  
Semi Markov Processes

Let (I(t))∞t = () be a semi-Markov process with state space II and recurrent probability transition kernel P. Subject to certain mixing conditions, where Δis an invariant probability measure for P and μb is the expected sojourn time in state b ϵΠ. We show that this limit is robust; that is, for each state b ϵ Πthe sojourn-time distribution may change for each transition, but, as long as the expected sojourn time in b is µb on the average, the above limit still holds. The kernel P may also vary for each transition as long as Δis invariant.

An invariance principle for semi-Markov processes

1985 ◽  
Vol 17 (01) ◽  
pp. 100-126
Author(s):  
D. McDonald
Keyword(s):  
Sojourn Time ◽  
Time Distribution ◽  
Invariant Probability Measure ◽  
Transition Kernel ◽  
Mixing Conditions ◽  
Sojourn Time Distribution ◽  
Semi Markov Process ◽  
Image Position ◽  
Expected Sojourn Time ◽  
Semi Markov Processes

Let (I(t))∞ t = () be a semi-Markov process with state space II and recurrent probability transition kernel P. Subject to certain mixing conditions, where Δis an invariant probability measure for P and μ b is the expected sojourn time in state b ϵΠ. We show that this limit is robust; that is, for each state b ϵ Πthe sojourn-time distribution may change for each transition, but, as long as the expected sojourn time in b is µ b on the average, the above limit still holds. The kernel P may also vary for each transition as long as Δis invariant.

Partially observable semi-Markov reward processes

1993 ◽  
Vol 30 (3) ◽  
pp. 548-560 ◽  
Author(s):  
Yasushi Masuda
Keyword(s):  
Markov Process ◽  
Counting Process ◽  
Probabilistic Interpretation ◽  
Real Domain ◽  
Semi Markov Process ◽  
Reward Process ◽  
Markov Reward ◽  
Partially Observable ◽  
Joint Behavior

The main objective of this paper is to investigate the conditional behavior of the multivariate reward process given the number of certain signals where the underlying system is described by a semi-Markov process and the signal is defined by a counting process. To this end, we study the joint behavior of the multivariate reward process and the multivariate counting process in detail. We derive transform results as well as the corresponding real domain expressions, thus providing clear probabilistic interpretation.

Partially observable semi-Markov reward processes

1993 ◽  
Vol 30 (03) ◽  
pp. 548-560 ◽  
Author(s):  
Yasushi Masuda
Keyword(s):  
Markov Process ◽  
Counting Process ◽  
Probabilistic Interpretation ◽  
Real Domain ◽  
Semi Markov Process ◽  
Reward Process ◽  
Markov Reward ◽  
Partially Observable ◽  
Joint Behavior

The main objective of this paper is to investigate the conditional behavior of the multivariate reward process given the number of certain signals where the underlying system is described by a semi-Markov process and the signal is defined by a counting process. To this end, we study the joint behavior of the multivariate reward process and the multivariate counting process in detail. We derive transform results as well as the corresponding real domain expressions, thus providing clear probabilistic interpretation.

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