Systems often have two or more stages and a customer must go several stages before finalizing their service. The systems can be arranged in series or in network. Chapter 5 is dedicated specifically to the performance analysis of systems that have several stages both in series and those that have network arrangement; the theorems of Burke and Jackson are presented; the calculations of the flow and variability in a network and of the measures of performance (cycle time and work in process) are also exposed. Several codes are proposed in Scilab Language to perform calculations automatically. The chapter ends with a section devoted to identifying and analyzing the bottleneck in a system from a cost approach.
TopMulti-Stage Models
In the earlier chapters, we looked at queues under the assumption that the system consists of a single stage, in other words, when the customer leaves the station, its transformation process is finished and it does not need to go through a further stage, so it leaves the system.
However a customer usually requires several stages to complete its transformation process or sometimes has to return to one of the stations to repeat a process, in other words, to undergo a reprocess. There are a variety of systems where the customers may start its process through any of the stations, not necessarily through the one identified as station 1 and neither is it not necessary for the customers go through all the stages as they can also leave the system through any of the stations that make up the network (hence their name, open networks).
In the analysis of the performance and administration of a system formed by queues with several stages, it is vital to use indicators that enable us to establish its behavior, in order to give the decision-makers elements to support their decisions, such as increased capacity, the effect of reworks or the result of changes in demand. When making decisions, managers, administrators and, in general, everyone who is responsible for a system focuses on specific performance measures, for example:
- 1.
Total Work in Process (1): The average number of customers in the system, which is the sum of the accumulated work of each station.
(1) - 2.
Cycle Time (2): The period from when the customer enters the first stage of the process until it leaves the system. The time that an order takes, from the moment it enters the system until the product is delivered, is a much-used measurement for service quality.
(2) - 3.
Production Rate or Throughput (3): The number of pieces produced per unit of time. In the case of lines that do not have any constraint on the number of customers that can stay in the queue
(3)