A note on queues with M/G/∞ input

Performance analysis of a Poisson–Pareto queue over the full range of system parameters

“…Large Deviations Theory was used in [22] to obtain a consistent result for overflow probabilities. Related results have been obtained in [15,18].…”

“…Large buffer large deviations limit buffer size → ∞ [5, 6, 15, 21-23, 25, 26, 31] Many sources large deviations limit n → ∞; buffer size & C linear in n [10,[17][18][19][32][33][34] Heavy Traffic & CLT limit n → ∞; buffer size & net mean input linear in √ n [7,8,39,40] Heavy Traffic non CLT limit ρ → 1 and buffer size ∼ (1 − ρ)…”

“…This asymptotic regime is widely referred to as the Large Buffer Limit. The papers [10,[17][18][19][32][33][34] consider the case where the buffer size and server speed are linear in the number of sources, which tends to infinity. This is generally known as the Many Sources Limit.…”

“…One of these approaches was discussed in the previous subsection. The other approach has been used in [10,15,[17][18][19][32][33][34]. In this approach the limit is taken as n −→ ∞ where n is the number of sources, and the buffer threshold is assumed to grow in linear proportion to n also.…”

Performance evaluation of a queue fed by a Poisson Pareto burst process

“…Examples of this approach may be found in the work of Tsoukatos and Makowski [25], Parulekar and Makowski [20], González-Arévelo and Samorodnitsky [9] and Mandjes [15]. In [29], Tsybakov and Georganas use a large deviations approach to find expressions for both upper and lower bounds of the queueing performance of a finite buffer single server queue (SSQ) fed by an M/G/∞ process.…”