2025/05/27 by Manisha Dhillon, Dhillon, Manisha, Kuldeep Kumar Kataria +1
Business, Management and Accounting · Computer Science · Decision Sciences · #26A33 #60K25 #Advanced Queuing Theory Analysis #FOS: Mathematics #Interconnection Networks and Systems #Primary: 60K15 #Probability (math.PR) #Scheduling and Timetabling Solutions #Secondary: 60K20
paper · pdf · doi:10.48550/arxiv.2505.21804
openalex publication_date 2025/05/27 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28
In this paper, we introduce and study a time-changed variant of the Erlang queue with multiple arrivals where the time-changing component used is the first hitting time of a tempered stable subordinator. The system of fractional difference-differential equations that governs its state probabilities is derived which is solved to obtain their explicit expressions. An equivalent representation in terms of phases and the mean queue length is obtained. For a particular case, the distribution of inter-arrival times, inter-phase times, sojourn times, busy period and that of conditional waiting times are derived.