论文信息 - Inequalities for queues with dependent interarrival and service times

Inequalities for queues with dependent interarrival and service times

Consider two queues with k servers. Inequalities between their sample paths and thence between the distribution functions of their waiting times and queue sizes are deduced from inequalities between the conditional distribution functions, given previous interarrival and service times, for the two queues. QUEUES; WAITING TIMES; STOCHASTIC ORDERING

G. O'Brien

[1] J. T. Runnenburg,et al. An example illustrating the possibilities of renewal theory and waiting-time theory for Markov-dependent arrival-intervals , 1961 .

[2] R. M. Loynes,et al. Stationary Waiting-Time Distributions for Single-Server Queues , 1962 .

[3] Lajos Takács,et al. General Stochastic Processes in the Theory of Queues , 1964 .

[4] P. A. P. Moran,et al. Two-Sided Inequalities for Waiting Time and Queue Size Distributions in $GI/G/1$ , 1968 .

[5] M. Neuts,et al. The infinite server queue with semi-Markovian arrivals and negative exponential services , 1972, Journal of Applied Probability.

[6] David R. Jacobs,et al. Stochastic Order Relationships Between GI/G/k Systems , 1972 .

[7] G. O'Brien. The Comparison Method for Stochastic Processes , 1975 .