A Monotonicity Theorem for Tandem Queues

Abstract:

Tandem queues are often used for performance modeling in production lines,
computer systems and communication networks. Consider a series of tandem
first-come-first-served queues with single servers. The buffers may be
finite or infinite. When a finite buffer is full, the upstream server may
suffer from transfer blocking or service blocking. A job's service
requirements at various servers may be correlated. A transient analysis shows
that, if the network is open, then response time decreases if a server is
speeded up, or a finite buffer increases in size, or service blocking is
changed to transfer blocking at some server; if the network is closed, then
such changes increase the throughput. The analytic technique is elementary,
and the equations can be used to simulate a network.