Analysis of the GI/Geo/1 Queue with Disasters

Abstract

The occurrence of disasters to a queueing system causes all customers to be removed if any are present. Although there has been much research on continuous-time queues with disasters, the discrete-time Geo/Geo/1 queue with disasters has appeared in the literature only recently. We extend this Geo/Geo/1 queue to the GI/Geo/1 queue. We present the probability generating function of the stationary queue length and sojourn time for the GI/Geo/1 queue. In addition, we convert our results into the Geo/Geo/1 queue and the GI/M/1 queue.

Keywords:

• Disaster
• Discrete-time queue
• GI/Geo/1
• Queue length PGF
• Sojourn time PGF

Mathematics Subject Classification:

• 60K25
• 68M20
• 90B22