Different from general operating policies to be applied for controllable queueing models, two of three well-known simple N, T and D operating policies are applied alternatingly to the single server controllable queueing models, so called alternating (NT), (ND) and (TD) policies. For example, the alternating (ND) operating policy is defined as the busy period is initiated by the simple N operating policy first, then the next busy period is initiated by the simple D operating policy and repeats the same sequence after that continuously. Because of newly designed operating policies, important system characteristic such as the expected busy and idle periods, the expected busy cycle, the expected number of customers in the system and so on should be redefined. That is, the expected busy and idle periods are redefined as the sum of the corresponding expected busy periods and idle periods initiated by both one of the two simple operating policies and the remaining simple operating policy, respectively. The expected number of customers in the system is represented by the weighted or pooled average of both expected number of customers in the system when the predetermined two simple operating policies are applied in sequence repeatedly. In particular, the expected number of customers in the system could be used to derive the expected waiting time in the queue or system by applying the famous Little’s formulas. Most of such system characteristics derived would play important roles to construct the total cost functions per unit time for determination of the optimal operating policies by defining appropriate cost elements to operate the desired queueing systems.

A steady-state controllable M/G/1 queueing model operating under the {T:Min(T,N)} policy is considered where the {T:Min(T,N)} policy is defined as the next busy period will be initiated either after T time units elapsed from the end of the previous busy period if at least one customer arrives at the system during that time period, or after T time units elapsed without a customer’ arrival, the time instant when Nth customer arrives at the system or T time units elapsed with at least one customer arrives at the system whichever comes first. After deriving the necessary system characteristics including the expected number of customers in the system, the expected length of busy period and so on, the total expected cost function per unit time for the system operation is constructed to determine the optimal operating policy. To do so, the cost elements associated with such system characteristics including the customers’ waiting cost in the system and the server’s removal and activating cost are defined. Then, procedures to determine the optimal values of the decision variables included in the operating policy are provided based on minimizing the total expected cost function per unit time to operate the queueing system under considerations.

A steady-state controllable M/G/1 queueing model operating under the (TN) policy is considered where the (TN) policy is defined as the next busy period will be initiated either after T time units elapsed from the end of the previous busy period if at least one customer arrives at the system during that time period, or the time instant when Nth customer arrives at the system after T time units elapsed without customers’ arrivals during that time period. After deriving the necessary system characteristics such as the expected number of customers in the system, the expected length of busy period and so on, the total expected cost function per unit time in the system operation is constructed to determine the optimal operating policy. To do so, the cost elements associated with such system characteristics including the customers’ waiting cost in the system and the server’s removal and activating cost are defined. Then, the optimal values of the decision variables included in the operating policies are determined by minimizing the total expected cost function per unit time to operate the system under consideration.

Using the known result of the expected busy period for a controllable M/G/1 queueing model operating under the triadic Max (N, T, D) policy, its upper and lower bounds are derived to approximate its corresponding actual value. Both bounds are represented

Us ing the known result of the expected bllsy period for the triadic Min (N, T, 0) operating po licy applied to a controllable M/GI1 queueing model, its upper and lower bounds are derived to approximate its corresponding ac tual value. 80th bounds are rep

Using the results of the expected busy periods for the dyadic Min(N, D) and Max(N, D) operating policies in a controllable M/G/1 queueing model, an important relation between them is derived. The derived relation represents the complementary property betw

The expected busy period for the controllable M/G/1 queueing model operating under the triadic Max (N, T, D) policy is derived by using a new concept so called “the pseudo probability density function.” In order to justify the proposed approaches for the

  The expected busy period for the controllable M/G/1 queueing model operating under the triadic policy is derived by using the pseudo probability density function which is totally different from the actual probability density function. In order to justif