{'fraction_non_alphanumeric': 0.02919020715630885, 'fraction_numerical': 0.010357815442561206, 'mean_word_length': 5.216374269005848, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Lattice Path Approach for Busy Period Density of GIb/G/1 Queues Using C2 Coxian Distributions

In this paper busy period analysis of non-Markovian queuing system GIb/G/1, starting initially with i0 batches of customers, is carried out via lattice path approach. Both interarrival and service time distributions are approximated by 2-phase Cox distributions, C2, that have Markovian property, amenable to the application of lattice paths combinatorial analysis. Arrivals occur in batches of size b. Distributions having rational Laplace-Stieltjes transform and square coefficient of variation lying in [1/2, ∞] form a very wide class of distributions. As any distribution of this class can be approximated by a C2, the use of C2, therefore, has led us to achieve results applicable to almost any real life queuing system GIb/G/1 occurring in computer systems, communication systems, manufacturing systems, etc. Numerical computations have been performed for different sets of values of the parameters involved using software Mathematica and presented graphically.