Efrat Perel and Uri Yechiali. 2_Queue Systems where Customers of One Queue Serve the Customers of the Other Queue submission

Abstract. 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, Q1, operates as a limited-buffer M(lambda1)/M(μ1)/1/N − 1
system. The other queue, Q2, has an unlimited buffer and receives
service from the customers of Q1. 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 L1 denote the number of customers in Q1.
Then, two models are studied, distinguished by their service discipline
in Q2: In Model 1, Q2 operates as an unlimited-buffer,
single-server M(lambda2)/M(μ2*L1)/1/infinity queue with
Poisson arrival rate lambda2 and dynamically changing service rate μ2*L1.
In Model 2, Q2 operates as an unlimited-buffer, multi-server
M(lambda2)/M(μ2)/L1/infinity queue with
(dynamically changing) L1 servers, each serving at a Poisson rate of μ2.
For both models we present two methods of analysis to derive the
system’s steady-state probabilities and for calculating the mean total
number of customers present in each queue: (i) via Probability Generating
Functions and (ii) via Matrix Geometric approach. Extreme
cases are indicated and numerical examples are presented.