A 24/7 widget repair facility is staffed by two repair technicians, one of whom

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A 24/7 widget repair facility is staffed by two repair technicians, one of whom is an expert and one of whom is a novice. The repair facility repair two types of widgets: basic ("B") widgets and advanced-technology ("AT") widgets Widgets needing repairs arrive at the facility with a mean interarrival time of 20 minutes (exponentially distributed). The probability that an arriving widget is a type B widget b 85 % and the probability that an arriving widget is a type AT widget is 15 % Arming widgets await service in a sing] queue (WTOGETQUF.UE) in FIFO order without regard to widget type. The WIDGETQUEUB is assumed to have infinite capacity. When a repair technician is/becomes available to provide service, the next widget needing repair - either an arriving widget if the WIDGETQUEUF is empty, or the widget at the front of the WIDGETQUEUE if the WIDGETQUEUE is nonempty -is assigned to that repair technician without regard to the widget's type. EXCEPT that if BOTH repair technicians are available to provide service, the next widget needing repair is assigned to the expert technician if it is an AT widget, or to the novice technician if it is a B widget. Widgets departing WIDGETQUEUE and commencing repair service receive uninterrupted service from their assigned repair technician until the repairs are completed. WITH THE FOLLOWING EXCEPTION: Whenever the novice technician commences repairs on an AT widget, the expert technician may in some eases immediately suspend work, on his/her current repair task (if any) and move to assist the novice in repairing that AT widget. Here are the three possible eases: If the expert technician is not currently working on a repair when the novice technician commences repairs on an AT widget, the expert immediately moves to assist the novice in repairing that AT widget, and continues to assist the novice (and is therefore unavailable to repair other widgets) until repairs on that AT widget are complete, at which time the expert becomes available again to work on repairing other widgets. If the expert technician is in the process of repairing a B widget when the novice technician commences repairs on an AT widget, the expert immediately moves to assist the novice in repairing that AT widget, and continues to assist the novice (and is therefore unavailable to continue work on repairing the B widget) until repairs on that AT widget are complete, at which time the expert returns to work repairing the B widget. We say the expat's work on the B widget was 'preempted" by the expert's assisting the novice with the novice's AT widget repairs. If the expert technician b in the process of repairing an AT widget when the novice technician commences repairs on an AT widget, the expert does not move to assist the novice, but instead continues working on his/her own AT widget until repairs on that AT widget are complete. The expert's work on his/her own AT widget repair is not preempted, and the novice works alone to complete the repairs on the novice's AT widget. The mean time required for the expat technician working alone to fix a type B widget is 5 minutes (exponentially distributed). The mean time required for the expert technician working alone to fix a type AT widget is 10 minutes (exponentially distributed). The mean time required for the novice technician working alone to fix a type B widget is 6 minutes (exponentially distributed). The mean time required for the novice technician working alone to fix a type AT widget is 12 minutes (exponentially distributed). The mean time required for the two technicians working together to fix a type AT widget is 8 minutes (exponentially distributed). How would eliminating the preemption procedure described above, and instead requiring that the expert and novice repair technicians always perform their assigned repairs without collaboration, affect the average down time (time spent awaiting repair plus time spent undergoing repair) for the two types of widgets? (Give answers to two decimal places; e.g. " 123.45") WITH PREEMPTION PROCEDURE Average down time for type B widgets is minutes. Average down time for type AT widgets is minutes. WITH NO COLLABORATION (NO PREEMPTION PROCEDURE) Average down time for type B widgets is minutes. Average down time for type AT widgets is minutes. Use GPSS simulation to arrive at answers to these questions. Explain your reasoning clearly and in detail, and DOCUMENT YOU WORK THOROUGHLY. See GPSS World Tutorial Lesson 4 ("TVREPAIR.CPS) for an example illustrating the implementation of preemption in GPSS.//end

Explanation / Answer

with preemption:

average downtime for the type B widgets is 5+6/2=11/5=5.50 minutes.This is calculated by taking the average of the total mean for the type B

average downtime for the type AT is 12+12/2=22/2=11.00 minutes which is the average of the total mean for the type AT

with no colloboration:

average time for the type B widgets is:6 miniutes as it has been stated which is the total mean

average time for the type AT widgets is10+8/2=9.00 minutes because we take colloboration and one without it and find their mean

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