On the Stability of Large MJQM With Correlated Arrivals

We compute the stability region of the Multiserver-Job Queuing Model (MJQM) with big and small jobs, first-in-first-out (FIFO) scheduling, and independent exponentially distributed job service times. Job arrivals follow a process with independent and generally distributed inter-arrival times and with non-independent selection of the job type. The type (big or small) of the next job to arrive depends on the type of the previously arrived job, so that a correlation exists in the sequence of job types. Our results use the saturation rule to show that in the case of a large number of servers, a positive correlation in the class of arriving jobs improves the MJQM stability region. Simulations with parameters derived from real data center operations show that this behavior appears also in much more complex and realistic settings.