Approximate Behavior of Tandem Queues

We consider two-stage tandem queuing systems with dedicated servers in each station and flexible servers that can serve in both stations. We assume exponential service times, linear holding costs, and operating costs incurred by the servers at rates proportional to their speeds. Under conditions that ensure the optimality of nonidling policies, we show that the optimal allocation of flexible servers is determined by a transition-monotone policy. Moreover, we present conditions under which the optimal policy can be explicitly determined.

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Tollbooth tandem queues with infinite homogeneous servers

Journal of Applied Probability ◽

10.1239/jap/1450802745 ◽

2015 ◽

Vol 52 (4) ◽

pp. 941-961 ◽

Cited By ~ 3

Author(s):

Xiuli Chao ◽

Qi-Ming He ◽

Sheldon Ross

Keyword(s):

Performance Measures ◽

System Performance ◽

Stochastic Ordering ◽

Tandem Queues ◽

Poisson Arrival ◽

Arrival Processes ◽

Poisson Arrivals ◽

Number Of Customers ◽

Steady State Solutions ◽

Transient And Steady State

In this paper we analyze a tollbooth tandem queueing problem with an infinite number of servers. A customer starts service immediately upon arrival but cannot leave the system before all customers who arrived before him/her have left, i.e. customers depart the system in the same order as they arrive. Distributions of the total number of customers in the system, the number of departure-delayed customers in the system, and the number of customers in service at time t are obtained in closed form. Distributions of the sojourn times and departure delays of customers are also obtained explicitly. Both transient and steady state solutions are derived first for Poisson arrivals, and then extended to cases with batch Poisson and nonstationary Poisson arrival processes. Finally, we report several stochastic ordering results on how system performance measures are affected by arrival and service processes.

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The dependence of sojourn times on service times in tandem queues

Journal of Applied Probability ◽

10.2307/3213628 ◽

1984 ◽

Vol 21 (3) ◽

pp. 661-667 ◽

Cited By ~ 2

Author(s):

Xi-Ren Cao

Keyword(s):

Sojourn Time ◽

Past History ◽

Interarrival Time ◽

Conditional Probabilities ◽

Tandem Queues ◽

Sojourn Times ◽

Distributed Service ◽

Service Times

In this paper we study a series of servers with exponentially distributed service times. We find that the sojourn time of a customer at any server depends on the customer's past history only through the customer's interarrival time to that server. A method of calculating the conditional probabilities of sojourn times is developed.

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