Abstract
We consider a real-world problem of military intelligence unit equipped with identical unmanned aerial vehicles producing real-time imagery and responsible for heterogeneous regions (with requests of real-time jobs) required to be under nonstop surveillance. Under certain assumptions these real-time systems can be treated as queueing networks.
The use of the system involving unmanned aerial vehicles relies on the principle of availability, namely on its ability to process the maximal portion of real-time tasks. We show that even very large number of vehicles does not guarantee the maximal system availability without proper choice of routing probabilities. We compute analytically (for exponentially distributed service and maintenance times) and via simulation using Cross-Entropy method (for generally distributed service times) optimal routing probabilities which maximize system availability.
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Abbreviations
- CE:
-
Cross Entropy
- CMC:
-
Crude Monte Carlo
- RTS:
-
Real-Time System
- UAV:
-
Unmanned Aerial Vehicle
- N :
-
Number of identical UAVs/servers
- r :
-
Number of heterogeneous regions/channels
- r k :
-
Number of real-time tasks/jobs in k-th region at any instant (r k ≥1)
- λ :
-
The maintenance rate (exponential distribution)
- μ k :
-
The service rate (exponential distribution) in the k-th region/channel
- p k :
-
Routing probability of a server to the k-th region/channel
- p * k :
-
Optimal routing probability of a server to the k-th region/channel
- λ k =λp k :
-
- ρ k =λ k /μ k :
-
- \(\frac{\rho _{u}}{r_{u}}=\max\mathrm{max}\,_{k=\overline{1,r}}\frac{\rho _{k}}{r_{k}}\) :
-
- \(\overline{n}=(n_{1},n_{2},\ldots,n_{r})\) :
-
State of RTS with r channels, where n k is a number of fixed servers assigned to the k-th channel ( \(k=\overline{1,r})\)
- \(p_{\overline{n}}=p_{n_{1},n_{2},\ldots,n_{r}}\) :
-
Steady-state probability of state (n 1,n 2,…,n r )
- \(\mathit{Av}_{N}(\bar{n},\rho_{1},\ldots,\rho_{r})\) :
-
System availability in state \(\bar{n}\) for RTS with N servers and r channels
- Av N (ρ1,…,ρ r ):
-
Average system availability for RTS with N servers and r channels
- Av(ρ1,…,ρ r ):
-
Limiting value (when N→∞) of Av N (ρ 1,…,ρ r )
- Av(ρ *1 ,…,ρ * r ):
-
Optimal value of Av(ρ 1,…,ρ r )
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Ianovsky, E., Kreimer, J. An optimal routing policy for unmanned aerial vehicles (analytical and cross-entropy simulation approach). Ann Oper Res 189, 215–253 (2011). https://doi.org/10.1007/s10479-009-0609-1
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DOI: https://doi.org/10.1007/s10479-009-0609-1