Regional Airlines está estableciendo un nuevo sistema telefónico para manejar las reservaciones de vuelos. Durante el periodo de 10:00 A.m. a 11:00 A.m. las llamadas del agente de reservaciones ocurren de forma aleatoria en un promedio de una llamada por cada 3.75 minutos, pasando el agente un promedio de 3 minutos por cliente.
La administración de Regional Airlines desea ofrecer un sistema de reservaciones eficiente, como parte de su orientación al servicio, pero no desea incurrir en un costo adicional al contratar persona que no sea necesario, ya que el costo por hora de un agente es de $20.00
Derivado de una reunión, el equipo de administración acordó una meta aceptable…show more content… 0.0595
f) THE PROBABILITY THAT AN ARRIVING UNIT HAS TO WAIT 0.2286
Modelo con 3 agentes (M/M/3)
NUMBER OF CHANNELS = 3
POISSON ARRIVALS WITH MEAN RATE = 16
EXPONENTIAL SERVICE TIMES WITH MEAN RATE = 20 PER CHANNEL
a) THE PROBABILITY OF NO UNITS IN THE SYSTEM 0.4472
b) THE AVERAGE NUMBER OF UNITS IN THE WAITING LINE 0.0189
c) THE AVERAGE NUMBER OF UNITS IN THE SYSTEM 0.8189
d) THE AVERAGE TIME A UNIT SPENDS IN THE WAITING LINE 0.0012
e) THE AVERAGE TIME A UNIT SPENDS IN THE SYSTEM 0.0512
f) THE PROBABILITY THAT AN ARRIVING UNIT HAS TO WAIT 0.0520
El planteamiento obtenido tenemos una tabla comparativa con los 3 modelos:
M/M/1 M/M/2 M/M/3 Probabilidad de que no haya clientes en el sistema Po 0.2000 (20%) 0.4286 (42.86%) 0.4472 (44.72%) Número promedio de clientes en línea en espera Lq 3.2000 0.1524 0.0189 Número de clientes promedio en el sistema L 4.0000 0.9524 0.8189
Tiempo promedio del cliente en la línea de espera Wq 0.2000 hrs (1.2 min) 0.0095 hrs (.57 min) 0.0012 hrs (0.072 min) Tiempo promedio del cliente en el sistema W 0.2500 hrs (15 min) 0.0595 hrs (3.57 min) 0.0512 hrs (3.072 min) Probabilidad de que un cliente deba esperar en la línea Pw 0.8000 (80%) 0.2286 (22.86%)
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