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- Title
SERVICE WAITING TIME AND FACTOR USE IN QUEUING SYSTEMS OF MARKOV TYPE.
- Authors
Bronza, Semen; Goncharova, Olga; Yurchak, Nataliya; Ovchiev, Murad
- Abstract
In many cases two variables such as utilization ratio (relative characteristic) and queuing time (absolute characteristic) are enough to assess the efficiency of a queuing system. The literature contains formulas for calculating utilization and downtime ratios as constants. In the paper, queuing time and utilization ratio are obtained as a function of time. This allows to investigate them in dynamics. For the queuing system S, set as a Markov chain with continuous time and finite number of states Ei i = 1,2,...,n, where n is the number of system state, the formulas for calculating the queuing time (downtime) in any state are obtained. Queuing time in the i-th state for the time interval ((τ, (τ) 12 can be calculated using the formula: Pi(τ1,τ2)=τ2∫τ1(Nqi(t)+ciλii)dt, and for the time t Pi(t)=t∫0(Nqi(t)+ciλii)dt The formulas for calculating the time of appearance and disappearance of queues, time intervals of the queue existence in any state of the system are obtained. The formulas for calculating the time of the beginning, end and duration of service in any state are obtained. The formulas of dependencies of utilization ratio of any system state on the time are obtained. Calculating the above functions for the unloading terminal of freight rail hub is given as an example of using the obtained formulas.
- Publication
Eastern-European Journal of Enterprise Technologies, 2014, Vol 3, Issue 4, p10
- ISSN
1729-3774
- Publication type
Article