ActaSATECH Journal of Life and Physical Sciences: ISSN: 15971007

On the relative mix transition probabilities in repairman problem of two different types with batch deterministic repairs

Authors: O Agboola S, O Obilade T,

Pages: (1-10 )


In this paper, the relative mix in the distribution of each machine type and the link between the durability and maintenance of each type of machine, are presented. Compared to existing machine repair problem, this study considered the repairman problem with multiple batch deterministic repairs of two different machine types 𝐴1 and 𝐴2. Without loss of generality, it is assumed that, there are integer 𝑘1 = 2 of type 𝐴1 machines and integer 𝑘2 = 2 of type 𝐴2 machines in the system such that 𝑘1 + 𝑘2 = 𝑘. Each type 𝐴1 (𝐴2) machine occasionally breaks down and moves into repair queue 𝑄1 (𝑄2) at Poisson rate 𝜆1(𝜆2). The Repair station has a capacity to repair at most two machines in a session. Flow balance equations are obtained for each of the 22 states of the system as defined by observing the system at repair time points. The resulting equations were solved for stationary probabilities at repair point and some server occupancy mode conditions using Gaussian elimination. Steady state repair completion mix probabilities (𝑝1 , 𝑝2 , 𝑝3 , ⋯ , 𝑝22 ) and steady state occupancy probabilities 𝑞𝑗 : 𝑗 = 1,2, ⋯ ,7 are obtained. Subsequently, the work are evaluated with adopted arrival rates 𝜆1 = 0.25, 0.50, 0.75, 1.00, ⋯ ,2.50 , 𝜆2 = 2.00, and specific deterministic repair times 𝐷𝑠𝑡 for 𝑠 and 𝑡 units of type 𝐴1 and 𝐴2 machines respectively. Using the Minkwoski distance of the various runs and system configuration as a guide, it was established that the closer the system is to a balanced situation the less is the discrepancy in the relative mix of the state probability distribution. We concluded that the relative mix can be rather different from each other depending on the appropriate parameter for the model.

Keywords: Machine repair problem; Flow balance equations; Occupancy mode condition; Relative mix.,

View Full PDF