TY - JOUR
T1 - Queues where customers of one queue act as servers of the other queue
AU - Perel, Efrat
AU - Yechiali, Uri
PY - 2008/12
Y1 - 2008/12
N2 - We consider a system comprised of two connected M/M/•/• type queues, where customers of one queue act as servers for the other queue. One queue, Q 1, operates as a limited-buffer M/M/1/N-1 system. The other queue, Q 2, has an unlimited-buffer and receives service from the customers of Q 1. Such analytic models may represent applications like SETI@home, where idle computers of users are used to process data collected by space radio telescopes. Let L 1 denote the number of customers in Q 1. Then, two models are studied, distinguished by their service discipline in Q 2: In Model 1, Q 2 operates as an unlimited-buffer, single-server M/M/1/∞ queue with Poisson arrival rate λ 2 and dynamically changing service rate μ 2 L 1. In Model 2, Q 2 operates as a multi-server M/M/L 1/∞ queue with varying number of servers, L 1, each serving at a Poisson rate of μ 2. We analyze both models and derive the Probability Generating Functions of the system's steady-state probabilities. We then calculate the mean total number of customers present in each queue. Extreme cases are indicated.
AB - We consider a system comprised of two connected M/M/•/• type queues, where customers of one queue act as servers for the other queue. One queue, Q 1, operates as a limited-buffer M/M/1/N-1 system. The other queue, Q 2, has an unlimited-buffer and receives service from the customers of Q 1. Such analytic models may represent applications like SETI@home, where idle computers of users are used to process data collected by space radio telescopes. Let L 1 denote the number of customers in Q 1. Then, two models are studied, distinguished by their service discipline in Q 2: In Model 1, Q 2 operates as an unlimited-buffer, single-server M/M/1/∞ queue with Poisson arrival rate λ 2 and dynamically changing service rate μ 2 L 1. In Model 2, Q 2 operates as a multi-server M/M/L 1/∞ queue with varying number of servers, L 1, each serving at a Poisson rate of μ 2. We analyze both models and derive the Probability Generating Functions of the system's steady-state probabilities. We then calculate the mean total number of customers present in each queue. Extreme cases are indicated.
KW - Connected 2-queue systems
KW - Customers act as servers
KW - Markovian queues
UR - http://www.scopus.com/inward/record.url?scp=57349175809&partnerID=8YFLogxK
U2 - 10.1007/s11134-008-9097-2
DO - 10.1007/s11134-008-9097-2
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AN - SCOPUS:57349175809
SN - 0257-0130
VL - 60
SP - 271
EP - 288
JO - Queueing Systems
JF - Queueing Systems
IS - 3-4
ER -