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- Title
Sample-path analysis of general arrival queueing systems with constant amount of work for all customers.
- Authors
Yao, Yi-Ching; Miao, Daniel
- Abstract
We consider a discrete-time queueing system where the arrival process is general and each arriving customer brings in a constant amount of work which is processed at a deterministic rate. We carry out a sample-path analysis to derive an exact relation between the set of system size values and the set of waiting time values over a busy period of a given sample path. This sample-path relation is then applied to a discrete-time $$G/D/c$$ queue with constant service times of one slot, yielding a sample-path version of the steady-state distributional relation between system size and waiting time as derived earlier in the literature. The sample-path analysis of the discrete-time system is further extended to the continuous-time counterpart, resulting in a similar sample-path relation in continuous time.
- Subjects
SAMPLE path analysis; SYSTEMS theory; SET theory; CONTINUOUS time systems; DISCRETE time filters; DISTRIBUTION (Probability theory)
- Publication
Queueing Systems, 2014, Vol 76, Issue 3, p283
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-013-9361-y