Dimensioning a queue with state-dependent arrival rates

In an observable queue, customers joining decisions may be influenced by wait-aversion and crowd-attraction. These opposing phenomena the diversity of arriving lead to arrival process that depends on number present customers. For system manager, having more beneficial as it can increase future arrivals due attraction generated. It also saturate system, resulting in long waits. Rejection at then employed a way obtain trade-off between these conflicting objectives. With this mind, we developed Markov decision approach determine how optimally reject queueing with state-dependent arrivals. When rate is bounded, compute optimal policy from value iteration approach. decreasing convex, prove has threshold form. increasing potentially unbounded, uniformization not apply. dealing case, restrict analysis stationary policies optimality computational addition, show within finite iterations long-run expected cost convex servers. We finally illustrate applicability our results through linearly rate, determining main drivers control decisions.