Geodesic
Conditions for the convergence to limit processes and the strong law of large numbers in the queuing systems
Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 3, pp. 559-570

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We consider queueing systems with refuses or with queues, restricted by a number $N\infty$ or non-restricted, with many service channels or with only one. The inter-arrival and service times form a stationary sequence of dependent or independent random variables with arbitrary distribution functions. The main results are conditions for the convergence of the queueing and waiting time processes to stationary ones and the strong law of large numbers for these processes and arbitrary functionals from them. 
@article{TVP_1976_21_3_a7,
     author = {I. Ahmarov and N. P. Leont'eva},
     title = {Conditions for the convergence to limit processes and the strong law of large numbers in the queuing systems},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {559--570},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1976_21_3_a7/}
}
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I. Ahmarov; N. P. Leont'eva. Conditions for the convergence to limit processes and the strong law of large numbers in the queuing systems. Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 3, pp. 559-570. http://geodesic.mathdoc.fr/item/TVP_1976_21_3_a7/