On estimates of the loss probability for an M/M/n queueing system with channels of different service productivity
Matematikos ir informatikos institutas |
| Date |
|---|
1996 |
Nagrinėjama n-kanalinė masinio aptarnavimo sistema su praradimais ir su skirtingo našumo kanalais, esant Puasono paraiškų srautui ir eksponentiniam paraiškos aptarnavimo laikui kanaluose. Praradimo tikimybė įvertinama iš apačios ir iš viršaus paprastų formulių pagalba. Gauti įvertinimai supaprastina atskirų kanalų įtakos analizę visai masinio aptarnavimo sistemai.
The queueing system theory is well developed. Such an important problem as the efficient of customer service in efficiency a multichannel queueing system with different productivity of service channels is well developed, too. Exact formulas are obtained from which the loss probability can be computed (if the input stream of customers distributed as Poisson and service time of the customer is the exponential service time). However, these formulas are very complex. So, in this paper, two theorems are proved, in which upper and lower estimates of the loss probability are presented. These estimates are simple formulas that don't become more complex with the growing number of service channels in the queueing system.