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The objective of the KPR agents are to learn themselves in the minimum(learning) time to have maximum success or utilization probability ($f$). Adictator can easily solve the problem with $f = 1$ in no time, by asking everyone to form a queue and go to the respective restaurant, resulting in nofluctuation and full utilization from the first day (convergence time $\tau =0$). It has already been shown that if each agent chooses randomly therestaurants, $f = 1 - e^{-1} \simeq 0.63$ (where $e \simeq 2.718$ denotes theEuler number) in zero time ($\tau = 0$). With the only available informationabout yesterday's crowd size in the restaurant visited by the agent (as assumedfor the rest of the strategies studied here), the crowd avoiding (CA)strategies can give higher values of $f$ but also of $\tau$. Several numericalstudies of modified learning strategies actually indicated increased value of$f = 1 - \alpha$ for $\alpha \to 0$, with $\tau \sim 1/\alpha$. We show hereusing Monte Carlo technique, a modified Greedy Crowd Avoiding (GCA) Strategycan assure full utilization ($f = 1$) in convergence time $\tau \simeq eN$,with of course non-zero probability for an even larger convergence time. Allthese observations suggest that the strategies with single step memory of theindividuals can never collectively achieve full utilization ($f = 1$) in finiteconvergence time and perhaps the maximum possible utilization that can beachieved is about eighty percent ($f \simeq 0.80$) in an optimal time $\tau$ oforder ten, even when $N$ the number of customers or of the restaurants goes toinfinity.

Achieving Maximum Utilization in Optimal Time for Learning or Convergence in the Kolkata Paise Restaurant Problem